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\begin{document}

{
\title{\Huge{
\textcolor{red}{\bf
Massive Primordial Black Holes, Dark Matter, and More...}\\
\tccyan{\bf (Old predictions and new data)
}\\
}}
\author{{\bf
\Huge{{\tcblue{A.D. Dolgov}}}}
\\[2mm]
\large {\bf
{ { NSU, Novosibirsk, 630090, Russia, 
}} }\\
{\bf { ITEP, Moscow, 117218, Russia}
}}
\date{\Large{{
\tccyan{\bf{
\begin{center}{
\tcviol{
UCLA Dark Matter 2018\\
Los Angeles, USA\\
21-23 February 2018}
}\end{center}
}
}}}}
}
\maketitle


\Huge{
{\bf

\npni
\tcblue{Two different but related subjects:}\\
\tcred{I. A mechanism of massive PBH formation much different from all others.}
\tcviol{The basement of PBH creation is build at inflation by making large isocurvature
fluctuations at relatively small scales, with practically vanishing density perturbations.}  \\
\tcmag{It is achieved by a simple modification of a popular scenario of baryogenesis.
Density perturbations are generated rather late after the QCF phase transition.}
\tcblue{The emerging universe looks like a piece of Swiss cheese, where holes are high baryonic 
density objects occupying a minor fraction of the universe volume.}

\npni
\tcblue{II. A review of new (and not only new) astronomical data which are in strong tension with the accepted 
standard  cosmological model.} \\
\tcviol{The data nicely fits the suggested\\ scenario of PBH formation.}\\
\tcred{More and more evidence in favor of massive and supermassive PBH in the universe
appears practically every week.}

\npni
\tcmag{Heretic predictions of 1993} \\ 
\tcblue{A.Dolgov,  J.Silk PRD 47 (1993) 4244} \\
\tcred{"Baryon isocurvature fluctuations at \\
small scales and baryonic dark matter" }\tccyan{also A.D. Dolgov, M. Kawasaki, N.~Kevlishvili, 
 Nucl.Phys. B807 (2009) 229,}
\tcred{"Inhomogeneous baryogenesis, cosmic antimatter, and dark matter"}\\
\tcblue{turned into the accepted faith since they became
supported by the recent astronomical data.
}\\
\tcmag{It allows to cure an avalanche of inconsistencies with 
the standard $\bm{\Lambda}$CDM.}

\npni
\tcviol{The model  predicts an abundant formation of heavy PBHs with}
\tcred{log-normal mass spectrum.}  \tcblue{An essential ingredient 
of the mechanism is the
preparation of the PBH seeds during cosmological inflation.}
Similar mass spectrum is sometimes assumed for stars but it is completely different physics.
%This is a highly non-trivial result. \\
\tccyan{Log-normal mass spectrum of PBHs was rediscovered
by S. Clesse, J.~Garcia-Bellido, Phys. Rev. D92, 023524 (2015).}
Now in many works such spectrum  is postulated without any justification.\\[3mm]
\tcred{NB: not only PBHs can be created but also compact stellar-like objects.
}

\npni
\tcblue{Quarter of century old predictions:}\\
\tcred{$\bullet$ {Primordial BHs make all or dominant part of dark matter (DM).}}\\
\tcviol{$\bullet$ { Black holes in the universe are mostly primordial (PBH).}}\\
\tccyan{$\bullet$ {Early QSO formation}.}\\
\tcmag{$\bullet$ {Early creation of metals and dust}.}\\
\tcblue{$\bullet$ {Seeding of large galaxies by supermassive PBH.}}\\
$\bullet$ Recently, AD \& K. Postnov:\\
\tcred{ Seeding of globular clusters by $\bm{10^3 - 10^4}$ BHs} 
\tccyan{and dwarfs by $\bm{10^4 - 10^5}$ BH.}\\[2mm]
\tcviol{A possible by-product: plenty of (compact) anti-stars, even in the Galaxy.}

\npni
\tcviol{10 billion year story in 10 minutes.}
%\tcblue{I. A brief review of high-z discoveries.} 
\tcblue{The observations of the last several years indicate that  the young universe at $\bm{z \sim 10}$ is grossly overpopulated 
with numerous:} \\
\tcred{1. Bright QSOs, alias supermassive BHs, up to $\bm{M \sim 10^{10} M_\odot}$,}\\
\tcviol{2. Superluminous young galaxies,}\\
\tcblue{3. Supernovae, gamma-bursters,}\\
and full of dust and heavy elements.\\
\tcmag{These facts are in good agreement with the predictions listed in the previous page,} 
but in tension with the SCM.

\npni
%Some examples of the data.\\ 
\tcblue{1. Supermassive BH, or QSO.}\\
\tcred{About 40 quasars with $\bm{z> 6}$ are known, with BH of %\\
$\bm{ 10^9 M_\odot}$ and $\bm{L \sim 10^{13-14} L_\odot}$.}
%\tcmag{The quasars are supposed to be supermassive black holes}
%%%\tccyan{The formation SMBH in such short time by conventional mechanisms looks problematic.}\\
\tcblue{Such black holes,
\tcred{when the Universe was less than one billion years old,} 
present substantial challenges to theories of the formation and growth of
black holes and the coevolution of black holes and galaxies.}
%\tcmag{Even the origin of SMBH in contemporary universe during 14 Gyr is difficult to explain.} \\
Non-standard accretion physics and the formation of massive seeds seem to be necessary.
Neither of them is observed in the present day universe.

\npni
Two years ago another huge QSO was discovered
\tcred{"An ultraluminous quasar with a twelve billion solar mass black hole at redshift 6.30".}
Xue-BingWu et al,
Nature 518, 512 (2015).\\
\tcblue{There is already a serious problem with formation of lighter and less luminous quasars}
\tcred{which is multifold deepened with this new "creature".}
\tcred{The new one with $\bm{M \approx 10^{10} M_\odot }$  makes the formation}
\tcblue{absolutely impossible in the standard approach.}


\npni
\tcviol{2. Galaxies observed at $\bm{z \sim 10}$:
}\\
\tccyan{a galaxy at \tcred{$\bm{z \approx 9.6}$}, which was created at $\bm{t_U < 0.5}$ Gyr;} \\
\tcviol{a galaxy at \tcred{$\bm{z \approx 11}$,} born at
%which was formed earlier than the universe age was 
$\bm{t_U \sim 0.4}$ Gyr, three times more luminous in UV than other galaxies at $\bm{z = 6-8}$.} 
\tcred{Unexpectedly early creation.} \\
Not so young but extremely luminous galaxy %was recently found:
{\tcred{$\bm{L= 3\cdot 10^{14} L_\odot }$;  $\bm{t_U \sim 1.3 }$ Gyr.}\\
\tcviol{Quoting the authors:} {\tccyan{The galactic seeds, or embryonic black holes, might be bigger than thought possible.}
Or another way to grow this big is to have gone on a sustained binge, consuming food 
faster than typically thought possible.  \tcmag{Low spin is necessary!}

\npni
\tcblue{According to the paper "Monsters in the Dark" }
D. Waters, et al, Mon. Not. Roy. Astron. Soc. 461 (2016), L51
\tccyan{density of galaxies at $\bm{z \approx 11}$ is 
$\bm{10^{-6} }$ Mpc$\bm{^{-3}}$, an order of magnitude higher than estimated from the data at lower z.}
\tcred{Origin of these galaxies is unclear.}\\
\tcviol{Very recently: M.A. Latif, M Volonteri, J.H. Wise, [1801.07685] 
"... halo has a mass of $\bm{ 3 \times 10^{10}~M_{\odot}}$ at $\bm{z=7.5}$;
MBH accretes only about 2200 $\bm{M_{\odot}}$ during 320 Myr.}


\npni
\tcblue{3. Dust, supernovae, gamma-bursters...}
\tcmag{Abundant dust is observed in several early  galaxies, e.g. in HFLS3 at $\bm{ z=6.34} $ and in
A1689-zD1 at $\bm{ z = 7.55}$.} \\
Catalogue of the observed dusty sources indicates that their number is an order of magnitude larger 
than predicted by the canonical theory.\\
\tcblue{Hence, prior to or simultaneously with the QSO formation a rapid star formation should take place.}
\tcmag{These stars should evolve to a large number of
supernovae enriching interstellar space by metals through their explosions}\\
\tccyan{which later make molecules and dust.}
%{(We all are dust from SN explosions, but probably at much later time.)}
%\tcblue{Another possibility is a non-standard BBN in bubbles with very high baryonic density, which allows for 
%formation of heavy elements beyond lithium.}

\npni
\tcred{Observations of high redshift gamma ray bursters (GBR) also indicate 
a high abundance of supernova at large redshifts.} 
\tcviol{The highest redshift of the observed GBR is 9.4 and there are a few more
GBRs with smaller but still high redshifts.}\\
\tccyan{The necessary star formation rate for explanation of these early
GBRs is at odds with the canonical star formation theory.}

\npni
%\tcblue{The list of the problems:}\\[4mm]
\tcviol{Problems of contemporary universe: }\\ 
%\tcmag{CONTEMPORARY UNIVERSE} \\[2mm]
%\begin{enumerate}
\tcred{1. SMBH in every large galaxy;
even 15 Gyr are not enough.} \\
\tcblue{2. SMBH in small galaxies and in almost EMPTY space, $\bm{M\sim 10^9 M_\odot}$.} \\
\tccyan{3. Stars older than the Galaxy and even one older than the Universe. }\\
{4. MACHOs (low luminosity 0.5 solar mass objects) \tcred{ - origin unknown.}} \\
\tcviol{ 5. %Problems with the  
BH mass spectrum in the Galaxy: unexpected maximum at $\bm{ M \sim 8 M_\odot}$.} \\
\tcred{6. Sources of the observed GWs. }\\
\tcblue{7. Intermediate mass BHs: $\bm{M \sim 10^3 M_\odot}$, in globular clusters and $\bm{M\sim 10^{4-5}}$ in
dwarf galaxies.}  %\tcmag{fourty found recently $\bm{10^7<M<3\cdpt 10^9}$, 1802.01567.}

\npni
AND RECENTLY MORE PUZZLES:\\
\tcblue{Several (four?) binaries of SMBH.}\\
\tcviol{Quasar quartet.}\\
\tccyan{Plane concentration of galactic-satellites?} \\ 
Massive BHs in dwarfs: \tcred{ten IMBH, $\bm{ M = 3\times10^4 - 2 \times10^5 M_\odot}$}
\tcmag{and fourty found recently $\bm{10^7<M<3\cdot 10^9}$ [Chandra, 1802.01567].}\\
\tcblue{${\bm{0.8\cdot 10^9 M_\odot}}$ BH in  \tcred{NEUTRAL} universe at $\bm{z=7.5}$
[1712.01860].}\\
\tcviol{Triple SMBH [1712.03909].}\\
\tcmag{Faint QSO, z=6, $\bm{M=10^9 M_\odot}$ needs either super-Eddington accretion or \\
$\bm{10^5 M_\odot}$ seed, 1802.02782.}


\npni
\tcviol{All these problems are uniquely and simply solved by the  mechanism of creation in the early universe
of massive PBHs and compact stellar-like
objects %formation in the very early universe,
suggested  in 1993 (A.D. and J.Silk).} \tccyan{Log-normal mass spectrum was predicted, which  became
very popular during last year or two:}
\be
\tcred{\bm{ 
\frac{dN}{dM} = \mu^2 \exp{[-\gamma \ln^2 (M/M_0)], }
}}
\nonumber
\label{dn-dM}
\ee
with only 3 parameters: $\bm{\mu}$, $\bm{\gamma}$,  $\bm{M_0}$.\\
\tcblue{Spectrum is practically model independent, it is determined by inflation.
and stochastic process of BH creation.} 

\npni
\tcblue{The model is based on the supersymmetric
(Affleck-Dine) scenario for baryogenesis}
\tcmag{modified by introduction of a general renormalizable coupling of the scalar baryon 
to the inflaton field:}
%\tccyan{It is discussed in more details in several our papers} \tcred{applied to an
%explanation of existence of the observed "old" objects in the young universe and
%all mentioned above puzzles in the contemporary Universe.}\\
%\tcviol{As a byproduct it may predict abundant antimatter objects in the Galaxy.}\\
%Affleck-Dine field $\bm \chi$ with CW potential coupled to inflaton $\bm \Phi$
%(AD and Silk; AD, Kawasaki, Kevlishvili):
\be 
\tcblue{\bm{
U = \tcred{g|\chi|^2 (\Phi -\Phi_1)^2}  +
\lambda |\chi|^4 \,\ln( \frac{|\chi|^2 }{\sigma^2 })
}} 
\nonumber\\
\tcblue{\bm{+\lambda_1 \left(\chi^4 + h.c.\right) + %\nonumber\\
(m^2 \chi^2 + h.c.). \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,
}}\nonu
\ee
%CP would be broken, if the relative phase of $\bm{\lambda_1}$ and 
%$\bm m$ is non-zero, otherwise one can
%``phase rotate'' $\bm \chi$ and come to real coefficients. 
%{Coupling to fermions may break CP.}\\
%\tcred{Coupling to inflaton is the general renormalizable one.}

\npni
\tcblue{Several events of GW registration by LIGO and Virgo has proven that
 GR works perfectly, existence of BHs and GWs is established,} 
%\tcred{but "in much wisdom is much grief", mostly created by GW150914.} \\
but revealed essentially  three problems of the SCM:\\
\tcmag{1. Origin of heavy BHs  ($\bm{\sim 30 M_\odot}$).}\\
\tcviol{2. Low spins of the coalescing BHs.}\\
\tccyan{3. Formation of BH binaries from the original stellar binaries.}\\
S.Blinnkov, A.D., N.Porayko, K.Postnov. \\
\tcviol{See however, 
T.Broadhurst, J.M. Diego, G. Smoot. 1802.05273.}
\tcred{Gravitational lensing of GW from log-normal BHs
with central mass $\bm{8 M_{\odot}}$.}

\npni
\tcred{The first problem is a heavy BH origin.} 
\tcblue{Such BHs are believed
to be created by massive star collapse,} though a convincing theory is still lacking.\\
\tcviol{To form so heavy BHs, the progenitors should have $\bm{M > 100 M_\odot}$
%have had masses two orders of magnitude higher than the solar mass 
and  a low metal abundance to avoid too much
mass loss during the evolution.} Such heavy stars might be present in
young star-forming galaxies \tcred{but they are not yet observed in sufficiently high number.} 
\tccyan{Maybe the mirror matter progenitors will do(!?).}

\npni
\tcred{ Another problem is the low value of the BH spins in GW150914.}
It strongly constrains astrophysical BH formation from close binary systems. \tcblue{However, the 
dynamical formation of double massive low-spin BHs in dense stellar clusters is not excluded, but difficult.} \\
\tcviol{The second reliable LIGO detection, GW151226,
turned out to be closer to the standard binary BH system.} \\
\tcred{The other three demonstrate the same property.}

\npni
\tcblue{Last but not the least, formation of BH binaries.} Stellar binaries were \\
formed from common interstellar gas clouds and are quite frequent in galaxies.
\tcviol{If BH is created through stellar collapse,} \tcred{a small non-sphericity results in a huge 
velocity of the BH and the binary is destroyed.} \\
%\tcviol{(Huge velocities of pulsars in the Galaxy.)}\\
\tcblue{BH formation from PopIII stars and subsequent formation of BH
binaries with 
$\bm{(36+29) M_\odot}$ is analyzed and 
found to be negligible. } \\
\tcmag{All these problems are solved if the observed sources of GWs are the binaries of
primordial black holes (PBH).}

\npni
\tcblue{Globular clusters and massive BHs.}\\
\tcred{Very recent news: BH with\\ 
$\bm{M \approx 2000 M_\odot}$ observed
in the core of the
globular cluster 47 Tucanae.}\\
\tcviol{Origin unknown.}\\
\tcblue{Our prediction (AD, K.Postnov):
if the parameters of the mass distribution of PBHs are chosen to fit the LIGO data and the density of
SMBH, then  the number of PBH with masses 
$\bm{(2-3)\times 10^3 M_\odot}$ is about $\bm{10^4-10^5 }$ per one SMPBH with mass $\bm{>10^4 M_\odot}$.}\\
\tcred{This density of IMBHs is sufficient to seed the formation of globular clusters in galaxies.}\\
%\tccyan{according to the published estimates, It is assumed that all PBH with \\
%$\bm{M > 10^4 M_\odot}$ strongly accreted matter and grew up to billion
%solar masses.}

\npni
\tcblue{Literature:}\\
%"we are now".}\\
\tcred{"Beasts in Lambda-CDM Zoo",}  Phys. Atom. Nucl., 80 (2017)  987; 1605.06749;\\
\tcmag{"Massive and supermassive black holes in the contemporary and early universe ..."}
%and the problems of cosmology and astrophysics"
Physics Uspekhi, 
%\\ DOI 10.3367/UFNe.2017.06.038153
and several conference talks in the arXive.


\npni
$$ $$
$$ $$
\hspace{3cm} \tcmag{THE (HAPPY?) END}\\
$$ $$

More below for another 106 minutes

%\npni
\begin{figure}[tbp]
\begin{center}
\includegraphics[scale=0.7]{constraint_notes.pdf}
\caption{Constraints on PBH fraction in DM, $f=\rho_{\rm PBH}/\rho_{\rm DM}$,
where the PBH mass distribution is taken as
$\rho_{\rm PBH}(M)=M^2dN/dM$ %(see \cite{2016arXiv160706077C}).
The existing constraints (extragalactic $\gamma$-rays from evaporation (HR),
femtolensing of $\gamma$-ray bursts (F),
neutron-star capture constraints (NS-C), MACHO, EROS, OGLE microlensing (MACHO, EROS)
survival of star cluster in Eridanus II (E),
dynamical friction on halo objects (DF),
and accretion effects (WMAP, FIRAS))
%are taken from \cite{2016arXiv160706077C}
%and reference therein. 
The PBH distribution is shown for ADBD parameters $\mu=10^{-43}$~Mpc$^{-1}$,
$M_0=\gamma+0.1\times\gamma^2-0.2\times\gamma^3$ with $\gamma=0.75-1.1$ (red solid lines),
and $\gamma=0.6-0.9$ (blue solid lines).}
\label{f:PBH}
\end{center}
\end{figure}
%\npni
\begin{figure}[tbp]
\begin{center}
\includegraphics[scale=0.65]{bounds-text.pdf}
\end{center}
%\caption{Merging rate of binary BH (1/Gpc${^{3}}$/yr) per logarithmic mass interval over the universe age. The observed LIGO event rate is shown by the %purple rectangle.}
%\label{S1}
\end{figure}



\npni
\tcblue{Globular clusters and massive BHs.}\\
\tcred{Very recent news: BH with\\ 
$\bm{M \approx 2000 M_\odot}$ observed
in the core of the
globular cluster 47 Tucanae.}\\
\tcviol{Origin unknown.}\\
\tcblue{Our prediction (AD, K.Postnov):
if the parameters of the mass distribution of PBHs are chosen to fit the LIGO data and the density of
SMBH, then  the number of PBH with masses 
$\bm{(2-3)\times 10^3 M_\odot}$ is about $\bm{10^4-10^5 }$ per one SMPBH with mass $\bm{>10^4 M_\odot}$.}\\
\tcred{This density of IMBHs is sufficient to seed the formation of globular clusters in galaxies.}\\



\npni
\tcblue{Summary of limits on MACHOs}\\[3mm]
\tccyan{ ${\bm f}$ =  mass ratio of MACHOS to DM.}
Macho group:
\tcred{ $\bm{ 0.08<f<0.50 }$ (95\% CL)} 
\tcmag{for $\bm{0.15M_\odot < M < 0.9M_\odot} $;}\\
EROS: \tccyan{$\bm{f<0.2}$, $\bm{ 0.15M_\odot < M < 0.9M_\odot}$;}\\
EROS2:\tcblue{$\bm{ f<0.1}$,~$\bm{10^{-6}M_\odot<M<M_\odot}$;}\\
AGAPE: \tcred{$\bm{0.2<f<0.9}$,\\ 
for $\bm{0.15M_\odot < M < 0.9M_\odot} $;}\\
EROS-2 and OGLE: \tcmag{$ \bm{f <0.1} $ for  $\bm{M\sim 10^{-2} M_\odot}$ and
$\bm {f <0.2} $ for  $\bm{ \sim 0.5 M_\odot}$.}



\end{document}

%DSP

\npni
%\tcblue{ABSTRACT}\\
%The review is presented on the 
Astronomical data accumulated mostly during several recent years are in 
striking disagreement with the standard cosmology and astrophysics. \\
\tccyan{"Something is rotten in the cosmological kingdom"  (almost Shakespeare).}\\
{Heretic conclusions:}\\
\tcblue{1) Black holes in the universe are mostly primordial (PBH);}\\
\tcred{2) Primordial BHs makes all or dominant part of dark matter (DM).}\\
\tcviol{Simple mechanism of resolution of the observed tension with the standard cosmology is presented} 
\tccyan{(in fact it was predicted a quarter of century ago, AD, J.Silk 1993.)}

\npni
%\tcblue{Astronomical data accumulated mostly during a few recent years
%very strongly indicate that the bulk of black holes in the universe are}
%\tcred{primordial. }\\
The usual black holes observed in contemporary universe 
are assumed to be created in the process of the star collapse  of stars with the masses $\bm{\gtrsim 3M_\odot}$.\\
\tcmag{Supermassive BHs (SMBH) with masses $\bm{(10^6-10^9) M_\odot}$,
"living" in galactic centers, might be formed by matter accretion to the center,} 
\tcblue{(not supported by calculations).}\\
\tcviol{PBH are formed at prestellar epoch if $\bm{\delta\rho/\rho \sim 1}$ at horizon (Zeldovich, Novikov). Their masses  can vary 
from a fraction of gram up to supermassive BH mass.}

\npni
%PART I.\\[3mm]
\tcred{The observations of several recent years revealed multitude of objects which, 
according to the standard approach, could not exist in our universe:}
\tcblue{they are either much younger or much older than allowed  by the theory.}
%\tcviol{Even if they might exist, they possess quite unexpected properties.} 
\\
\tcviol{The problems persist both in the  present day universe and in the young universe, $\bm{\sim 20}$ 
times younger than $\bm{t_U}$.} \\
%"we are now".}\\
More details:  \tcred{"Beasts in Lambda-CDM Zoo",}  Phys. Atom. Nucl., 80 (2017)  987; arXiv:1605.06749:\\
\tcmag{"Massive and supermassive black holes in the contemporary and early universe ..."}
%and the problems of cosmology and astrophysics"
Physics Uspekhi, \\ DOI 10.3367/UFNe.2017.06.038153.

\npni
\tcblue{The list of the problems:}\\[4mm]
\tcmag{I. CONTEMPORARY UNIVERSE} \\[2mm]
%\begin{enumerate}
\tcred{1. SMBH in every large galaxy.} \\
\tcblue{2. SMBH in small galaxies and in almost EMPTY space, $\bm{M\sim 10^9 M_\odot}$.} \\
\tccyan{3. Stars older than the Galaxy and even older than the Universe. }\\
{4. MACHOs (low luminosity 0.5 solar mass objects) \tcred{ - origin unknown.}} \\
\tcviol{ 5. %Problems with the  
BH mass spectrum in the Galaxy: unexpected maximum at $\bm{ M \sim 8 M_\odot}$.} \\
\tcred{6. Sources of the observed GWs. }\\
\tcblue{7. Intermediate mass, $\bm{ \sim 10^3 M_\odot}$, BHs in globular clusters. }\\


\npni
\tcviol{All these problems are uniquely and simply solved by the  mechanism of creation in the early universe
of massive PBHs and compact stellar-like
objects %formation in the very early universe,
suggested  in 1993 (A.D. and J.Silk).} \tccyan{Log-normal mass spectrum was predicted, which  became
very popular during last year or two:}
%\npni
%The distributions of high baryon density bubbles over length 
%and mass have log-normal form:
\be
\tcred{\bm{ 
\frac{dN}{dM} = \mu^2 \exp{[-\gamma \ln^2 (M/M_0)], }
}}
\nonumber
\label{dn-dM}
\ee
with only 3 parameters: $\bm{\mu}$, $\bm{\gamma}$,  $\bm{M_0}$.\\
\tcblue{Spectrum is practically model independent, it is determined by inflation.
and stochastic process of BH creation.} 


\npni
\tcblue{MYSTERIES IN THE SKY TODAY AND IN THE NEAREST PAST. } \\ [2mm]
\tccyan{ Every large galaxy %and some smaller ones 
contains a central supermassive BH with
mass  larger than} 
\tcred{ $\bm{ 10^{9}M_\odot}$} in giant elliptical
and compact lenticular galaxies
and \tcred{$\bm{\sim10^6 M_\odot}$} in spiral galaxies like Milky Way.\\
\tcred{The origin of these BHs is not understood.}
\tcviol{Accepted faith is that
these BHs are created by matter accretion to a central seed. }
\tcblue{But, the usual accretion efficiency is insufficient to create them during the Universe life-time,
14 Gyr.} \\
\tcmag{Even more puzzling: SMHBs  are observed  in small galaxies
 and even in almost \tccyan{EMPTY} space, where no material to make a SMBH can be found.}

\npni
\tcred{Some examples of the data:}\\
\tcblue{The mass of BH is typically 0.1\% of the mass of the stellar bulge of galaxy} 
% \cite{BH-bulge,*SaniMarconi}
but some galaxies may  have huge BH: \tcred{e.g. NGC 1277  has
the central BH  of  $\bm{1.7 \times 10^{10} M_\odot}$, or $\bm{60}$\% of its bulge mass.}
%\cite{NGC1277}.
\tcblue{This creates serious problems for the
standard scenario of formation of central supermassive BHs by accretion of matter in the central 
part of a galaxy.}\\
\tcviol{An inverted picture is more plausible, when first a supermassive BH was formed and 
attracted matter being a seed for subsequent galaxy formation!!!}\\

\newn
\tcblue{More examples:}\\
F. Khan, et al
%K. Holley-Bockelmann,  P. Berczik 
arXiv:1405.6425.CLUSIO
Although supermassive black holes
correlate well with their host
galaxies, there is an emerging view that outliers exist.
\tcblue{ Henize 2-10, NGC 4889,
and NGC1277 are examples of SMBHs at least \tcmag{AN ORDER OF MAGNITUDE MORE MASSIVE}  
%an order of magnitude more massive
than their host galaxy suggests. }
\tcred{The dynamical effects of such ultramassive central black holes is unclear. }


\newn
\tcblue{A recent discovery of an ultra-compact dwarf galaxy
older than 10 Gyr, enriched with metals, and probably with a massive black in its center} 
\tcred{seems to be at odds with the standard model}
J. Strader,  {\it et al} %A. C. Seth, D. A. Forbes, G. Fab- biano, A. J. Romanowsky, J. P. Brodie, C. Conroy, 
%N. Caldwell,  V. Pota, C. Usher, and J. A. Arnold, 
 Ap. J. Lett. 775, L6 (2013). \\
\tcblue{The dynamical mass is $\bm{2\times 10^8 M_\odot}$ 
and  $\bm{R \sim 24}$ pc -}  \tcred{very high density.}\\
Chandra: variable central X-ray source with \tcred{ $\bm{L_X \sim 10^{38}}$ erg/s,} which may be
\tcblue{an AGN associated with a massive black hole} or a low-mass X-ray binary.

\npni
\tcblue{"An evolutionary missing link? A modest-mass early-type
galaxy hosting an over-sized nuclear black hole",}
J. Th. van Loon, A.E. Sansom,
Xiv:1508.00698v1 %[astro-ph.GA] 4 Aug 2015.\\ 
\tcred{BH mass, $\bm{M_{BH} = (3.5 \pm 0.8) \cdot 10^8 M_\odot}$,}
\tcblue{host galaxy $\bm{M_{stars} = 2.5^{+2.5}_{-1.2} \cdot 10^{10} M_\odot}$,}
and accretion luminosity: \\
\tcred{$\bm{ L_{AGN} = (5.3 \pm 0.4) \cdot 10^{45} }$erg/s $\bm{\approx 10^{12} L_\odot}$.}\\
%(12\% of the Eddington luminosity). 
\tcblue{The AGN is more prominent than expected for a host galaxy
of this modest size.} The data are in tension with the accepted picture in which
this galaxy would recently have transformed from a star-forming disc galaxy into an
early-type, passively evolving galaxy.

\npni
%\tcblue{Very fresh publication:}
\tcred{"A Nearly Naked Supermassive Black Hole"} J.J. Condon, et al %J. Darling, Y. Y. Kovalev, L. Petrov,
arXiv:1606.04067.
\tcblue{A compact symmetric radio source B3 1715+425
is too bright (brightness temperature $\bm{\sim 3\times10^{10}}$ K at observing frequency 7.6 GHz) and too luminous (1.4 GHz 
luminosity $\bm{\sim 10^{25}}$ W/Hz) }
\tcmag{to be powered by anything but a SMBH, but its host galaxy is much smaller. }

\npni
\tcblue{Several binaries of SMBH observed:}\\[2mm]
\tcred{P. Kharb, et al
"A candidate sub-parsec binary black hole in the Seyfert galaxy NGC 7674", d=116 Mpc,
 $\bm{3.63\times 10^7 M_\odot}$.  (1709.06258).}\\
\tcviol{C. Rodriguez et al. A compact supermassive binary black hole system. Ap. J. 646,
49 (2006),  $\bm{d \approx 230}$~Mpc.}\\
\tccyan{M.J. Valtonen, "New orbit solutions for the precessing binary black hole model of OJ 287",
Ap.J. 659, 1074 (2007), $\bm{z \approx 0.3}$.}\\
\tcmag{M.J. Graham et al. "A possible close supermassive black-hole binary in a quasar with
optical periodicity". Nature 518, 74 (2015),  $\bm{z \approx 0.3}$.}

\npni
\tcblue{Orthodox point of view:}
\tccyan{merging of two spiral galaxies creating an elliptical
galaxy, leaving two or more SBHs in the center of the merged elliptical.}
No other way in the traditional approach. Even one SMBH is hard to create.
\\[2mm]
\tcviol{Heretic but simpler:} \tcred{primordial SMBH forming binaries in the very early universe and 
seeding galaxy formation.}



\newn
\tcblue{Old stars in the Milky Way:}\\[3mm]
Employing thorium and uranium % abundances
in comparison with each other and with several stable elements \tcblue{the age of
metal-poor, halo star BD+17$^o$ 3248 was estimated as}  \tcred{ $\bm{13.8\pm 4}$ Gyr.}\\
% "The chemical composition and age of the metal-poor halo star BD+17$^o$ 3248"
J.J. Cowan, %C. Sneden, S. Burles, 
{\it et al}
Ap.J. 572 (2002) 861 %, astro-ph/0202429. 
\\[3mm]
\tcblue{The age of inner halo of the Galaxy} \tcred{$\bm{11.4\pm 0.7}$ Gyr,} J. Kalirai, 
"The Age of the Milky Way Inner Halo"
Nature 486 (2012) 90, arXiv:1205.6802.

\newn
\tcred{The age of a star in the galactic halo, HE 1523-0901, was estimated to be 
about 13.2 Gyr.}
\tcblue{First time many different chronometers, such as the U/Th, U/Ir, Th/Eu and Th/Os ratios to
measure the star age have been employed.}\\[3mm]
"Discovery of HE 1523-0901: A Strongly r-Process Enhanced Metal-Poor Star with Detected Uranium",
A. Frebe, N. Christlieb, J.E. Norris, C. Thom  Astrophys.J. 660 (2007) L117;
astro-ph/0703414. 

\newn
Metal deficient \tcblue{high velocity} subgiant in the solar neighborhood
HD 140283  has the age \tcred{$\bm{14.46 \pm 0.31 }$ Gyr.}\\
H. E. Bond, %E. P. Nelan, D. A. VandenBerg, G. H. Schaefer,  D. Harmer, 
et al, Astrophys. J. Lett. 765, L12 (2013), arXiv:1302.3180.\\
\tcred{The central value exceeds the universe age by two standard deviations,
if $\bm{H= 67.3}$ and $\bm{t_U =13.8}$;}
\tcblue{and if $\bm{H= 74}$, then $\bm{ t_U = 12.5}$, more than 10 $\bm{\sigma}$} \\
\tcmag{Our model predicts unusual  initial chemical content of the stars, so they may look older than they are.}

\npni
X. Dumusque, {\it et al}
\tcblue{"The Kepler-10 Planetary System Revisited by \\
HARPS-N: A Hot Rocky World and a Solid Neptune-Mass Planet".}\\
arXiv:1405.7881; Ap J., 789, 154, (2014).
\tcred{Very old planet, $\bm{10.6^{+1.5}_{-1.3} }$ Gyr.}\\
\tcblue{(Age of the Earth: 4.54 Gyr.)} \\
\tcred{A SN explosion must must precede  formation of this planet.}

\npni
%Natural explanation of 
%%MACHOS - invisible stellar mass objects observed by gravitational  micorlensing.\\
%too many for low luminosity  stars.
%\tcblue{MACHOs.}
%%A similar or maybe even connected problem is related to the nature of
\tcred{ MACHOs: discovered through 
gravitational microlensing by Macho and Eros groups.}
\tccyan{They are invisible (very weakly luminous or even non-luminous) objects} \tcviol{with
masses about a half of the solar mass} 
\tcmag{in the Galactic halo, in the center of the Galaxy, and recently in
the Andromeda (M31) galaxy. }
\tcblue{Their density is  significantly greater than the density expected from the known low luminosity
stars and the usual BH of similar mass.} 


\npni
\tcblue{Summary of limits on MACHOs}\\[3mm]
\tccyan{ ${\bm f}$ =  mass ratio of MACHOS to DM.}
Macho group:
\tcred{ $\bm{ 0.08<f<0.50 }$ (95\% CL)} 
\tcmag{for $\bm{0.15M_\odot < M < 0.9M_\odot} $;}\\
EROS: \tccyan{$\bm{f<0.2}$, $\bm{ 0.15M_\odot < M < 0.9M_\odot}$;}\\
EROS2:\tcblue{$\bm{ f<0.1}$,~$\bm{10^{-6}M_\odot<M<M_\odot}$;}\\
AGAPE: \tcred{$\bm{0.2<f<0.9}$,\\ 
for $\bm{0.15M_\odot < M < 0.9M_\odot} $;}\\
EROS-2 and OGLE: \tcmag{$ \bm{f <0.1} $ for  $\bm{M\sim 10^{-2} M_\odot}$ and
$\bm {f <0.2} $ for  $\bm{ \sim 0.5 M_\odot}$.}


\npni
\tcblue{Thus MACHOs for sure exist.} \\
\tcmag{Their density is comparable to the density of the halo dark matter but their nature is unknown.}\\
They could be brown dwarfs,  dead stars, or primordial black holes. \\
\tcred{The first two options are in conflict with the accepted theory of stellar evolution, if MACHOs 
were created in the conventional way.}


\npni
\tcblue{More mysteries:}\\
\tcred{It was found that the BH masses are concentrated in the narrow range \\
$\bm{ (7.8 \pm 1.2) M_\odot }$} (1006.2834)\\
This result agrees with another paper where
\tcblue{a peak around $\bm{8M_\odot}$, a paucity of sources with masses below
 $\bm{5M_\odot}$, and a sharp drop-off above
$\bm{10M_\odot}$ are observed,} arXiv:1205.1805.
\tcred{These features are not explained  in the standard model of BH
formation by stellar collapse,}
\tcviol{but nicely fit the hypothesis of primordial BH formation with log-normal spectrum and $\bm{M_0 \approx 8 M_\odot}$.}

\npni
\tcblue{Very fresh results:}
\tcmag{Lev Titarchuk, Elena Seifina, and Pascal Chardonnet,} 
Astronomy and Astrophysics, submitted.\\
\tccyan{Measurement of BH masses  through the  X-ray spectra from the Galactic BH binaries:}\\
\tcred{GRS 1915+105: $\bm{(14\pm 4) M_\odot}$;}\\
\tcblue{SS 433: $\bm{(4.30 \pm 0.8) M_\odot}$;}\\
\tcviol{V4641 Sgr: $\bm{(9.60 \pm 0.8) M_\odot}$.}

\npni
\tcblue{GW discovery by LIGO has proven thar
 GR works perfectly, existence of BHs and GWs is established,} 
\tcred{but "in much wisdom is much grief", mostly created by GW150914.} \\
There are essentially  three problems in the standard theory:\\
\tcmag{1. Origin of heavy BHs  ($\bm{\sim 30 M_\odot}$).}\\
\tcblue{2. Low spins of the coalescing BHs.}\\
\tcred{3. Formation of BH binaries from the original stellar binaries.}\\
S.Blinnkov, A.D., N.Porayko, K.Postnov.


\npni
\tcred{The first problem is a heavy BH origin.} 
\tcblue{Such BHs are believed
to be created by massive star collapse,} though a convincing theory is still lacking.\\
\tcviol{To form so heavy BHs, the progenitors should have $\bm{M > 100 M_\odot}$
%have had masses two orders of magnitude higher than the solar mass 
and  a low metal abundance to avoid too much
mass loss during the evolution.} Such heavy stars might be present in
young star-forming galaxies \tcred{but they are not yet observed in sufficiently high number.} 
\tccyan{Maybe the mirror matter progenitors will do(!?).}

\npni
\tcred{ Another problem is the low value of the BH spins in GW150914.}
It strongly constrains astrophysical BH formation from close binary systems. \tcblue{However, the 
dynamical formation of double massive low-spin BHs in dense stellar clusters is not excluded, but difficult.} \\
\tcviol{The second reliable LIGO detection, GW151226,
turned out to be closer to the standard binary BH system.} \\
\tcred{The other three demonstrate the same property.}

\npni
\tcblue{Last but not the least, formation of BH binaries.} Stellar binaries were \\
formed from common interstellar gas clouds and are quite frequent in galaxies.
\tcviol{If BH is created through stellar collapse,} \tcred{a small non-sphericity results in a huge 
velocity of the BH and the binary is destroyed.} \\
%\tcviol{(Huge velocities of pulsars in the Galaxy.)}\\
\tcblue{BH formation from PopIII stars and subsequent formation of BH
binaries with 
$\bm{(36+29) M_\odot}$ is analyzed and 
found to be negligible. } \\
\tcmag{All these problems are solved if the observed sources of GWs are the binaries of
primordial black holes (PBH).}



\npni
\tcviol{Very recent announcement}\\
\tcmag{I. Zolotukhin, seminar GAISh, 10/10/17.}\\
\tcblue{Discovery of several new IMBHs.}\\
 The X-ray accretion radiation registered by  and XMM-Newton
 was analyzed. \tccyan{It led to 
registration of 10 IMBH,  with 5 being new.}\\
\tcred{$\bm{ M = 3\times10^4 - 2 \times10^5 M_\odot}$ }\\
The only possibility of the standard scenario is the coalescence of BH with solar mass. It meets serious 
difficulties. \tcblue{ The observations  nicely fit our scenario.}

\npni
\tcblue{I. A brief review of high-z discoveries.} In short, the young universe happened to be grossly overpopulated. 
\\[3mm]
\tcviol{1. Several galaxies have been observed %at high redshifts,
with natural gravitational lens ``telescopes. A few examples:}\\
\tccyan{a galaxy at \tcred{$\bm{z \approx 9.6}$} which was created at $\bm{t_U < 0.5}$ Gyr}; \\
%when the universe was about 0.5 Gyr old} 
%(W. Zheng,  {\it  et al});\\
\tcviol{a galaxy at \tcred{$\bm{z \approx 11}$} has been detected at
%which was formed earlier than the universe age was 
$\bm{t_U \sim 0.4}$ Gyr, three times more luminous in UV than other galaxies at $\bm{z = 6-8}$.} 
%(or even shorter with larger H).} D. Coe {\it et al}
%%%%\tcblue{Moreover a galaxy at \tcred{$\bm{z \approx 11}$} has been observed
%%which was formed earlier than the universe age was { 0.41 Gyr} (or even shorter with larger H).}
D. Coe {\it et al}
 %A. Zitrin, M. Carrasco, {
%X. Shu, W. Zheng, M. Postman, L. Bradley, A. Koekemoer, R. Bouwens, T. Broadhurst et al,
"CLASH: Three Strongly Lensed Images of a Candidate $\bm{z \sim11}$ Galaxy",
Astrophys. J. 762 (2013) 32. \\%; e-Print: arXiv:1211.3663. \\
\tcred{Unexpectedly early creation.}



\npni
Not so young but extremely luminous galaxy %was recently found:
%\tcblue{"The most luminous galaxies discovered by WISE"} 
%Chao-Wei Tsai, P.R.M. Eisenhardt {\it et al}, \\
%arXiv:1410.1751, 8 Apr 2015.\\
{\tcred{$\bm{L= 3\cdot 10^{14} L_\odot }$;  $\bm{t_U \sim 1.3 }$ Gyr.}\\
%The new study outlines three reasons why the black holes in the ELIRGs could have grown so massive. First, they 
%may have been born big. In other words, 
{\tccyan{The galactic seeds, or embryonic black holes, might be bigger than thought possible.}
P. Eisenhardt: "How do you get an elephant?  One way is start with a baby elephant."
\tcred{The BH was already billions of $\bm{M_\odot}$ , when our universe was only a 
tenth of its present age of 13.8 billion years.}
"Another way to grow this big is to have gone on a sustained binge, consuming food 
faster than typically thought possible."  \tcmag{Low spin is necessary!}

\npni
\tcblue{According to the paper "Monsters in the Dark" }
D. Waters, et al, Mon. Not. Roy. Astron. Soc. 461 (2016), L51
\tccyan{density of galaxies at $\bm{z \approx 11}$ is 
$\bm{10^{-6} }$ Mpc$\bm{^{-3}}$, an order of magnitude higher than estimated from the data at lower z.}\\
\tcred{Origin of these galaxies is unclear.}

\npni
\tcblue{2. Supermassive BH and/or QSO.}\\
About 40 quasars with $\bm{z> 6}$ are already known, each quasar containing BH with %\\
$\bm{M \sim 10^9 M_\odot}$. \\
The maximum z  is \tcred{$\bm{ z = 7.085}$}  i.e. the quasar was  
formed before the universe reached \tcblue{$\bm{0.75}$ Gyr with } \\
%Its luminosity and mass are: \\ 
\tcred{$\bm{L= 6.3 \cdot 10^{13} L_\odot}$,}
\tcred{$\bm{M=2 \cdot 10^9 M_\odot}$,}\\
%D.J. Mortlock, {\it et al}, " A luminous quasar at a redshift of z = 7.085"
%Nature 474 (2011) 616, arXiv:1106.6088 \\
Similar situation with the others.\\
\tcblue{The quasars are supposed to be supermassive black holes}
\tcred{and their formation in such short time by conventional mechanisms looks problematic.}

\npni
\tcblue{Such black holes,
\tcred{when the Universe was less than one billion years old,} 
present substantial challenges to theories of the formation and growth of
black holes and the coevolution of black holes and galaxies.}
\tcmag{Even the origin of SMBH in contemporary universe during 14 Gyr is difficult to explain.} \\
Non-standard accretion physics and the formation of massive seeds seem to be necessary.
Neither of them is observed in the present day universe.

%It is difficult to understand how {${10^9 M_\odot}$} black holes
%appeared so quickly after the big bang {without invoking non-standard accretion physics
%and the formation of massive seeds,} both of which are not seen in the local Universe.


\npni
Two years ago another huge QSO was discovered
\tcred{"An ultraluminous quasar with a twelve billion solar mass black hole at redshift 6.30".}
Xue-BingWu et al,
%Feige Wang, Xiaohui Fan, Weimin Yi, Wenwen Zuo, Fuyan Bian, Linhua Jiang, Ian D. McGreer, Ran Wang,
%Jinyi Yang, Qian Yang, David Thompson & Yuri Beletsky
Nature 518, 512 (2015).\\
%\tcred{Now we have $\bf{ 10^{10} M_\odot}$ !!!}
\tcblue{There is already a serious problem with formation of lighter and less luminous quasars}
\tcred{which is multifold deepened with this new "creature".}
\tcred{The new one with $\bm{M \approx 10^{10} M_\odot }$  makes the formation}
\tcblue{absolutely impossible in the standard approach.}

\npni
\tcblue{3. Dust, supernovae, gamma-bursters...}
\tccyan{To make dust a long succession of processes is necessary:} 
\tcred{first, supernovae  explode to deliver 
heavy elements into space (metals),} 
\tcblue{then metals cool and form molecules,}
\tcviol{and lastly molecules make macroscopic
pieces of matter.}\\
\tcmag{Abundant dust is observed in several early  galaxies, e.g. in HFLS3 at $\bm{ z=6.34} $ and in
A1689-zD1 at $\bm{ z = 7.55}$.} \\
Catalogue of the observed dusty sources indicates that their number is an order of magnitude larger 
than predicted by the canonical theory.

\npni
\tcblue{Hence, prior to or simultaneously with the QSO formation a rapid star formation should take place.}
\tcmag{These stars should evolve to a large number of
supernovae enriching interstellar space by metals through their explosions}\\
\tccyan{which later make molecules and dust.}
{(We all are dust from SN explosions, but probably at much later time.)}
\tcblue{Another possibility is a non-standard BBN in bubbles with very high baryonic density, which allows for 
formation of heavy elements beyond lithium.}


\npni
\tcred{Observations of high redshift gamma ray bursters (GBR) also indicate 
a high abundance of supernova at large redshifts.} 
\tcviol{The highest redshift of the observed GBR is 9.4 and there are a few more
GBRs with smaller but still high redshifts.}\\
\tccyan{The necessary star formation rate for explanation of these early
GBRs is at odds with the canonical star formation theory.}



\npni
\tcblue{All these problems are solved if the BHs in the universe and \tcred{stellar-like objects} are primordial, 
created at the very early stage, $\bm{ z  > 10}$.}\\
%the observed sources of GWs are the binaries of
%primordial black holes (PBH).}\\
%A model of their formation was proposed in our paper with J. Silk (1993).
\tccyan{According to our model the formation took place at very high $\bm{z}$ after the QCD phase transition at $\bm{T \sim 100}$ MeV 
down to $\bm{T \sim  }$ keV.}\\
%\tcred{It naturally reproduces the puzzling properties of GW150914,} 
%\tcviol{the rate of binary BH merging events inferred from the 
%first LIGO science run,} %9-240 Gpc$^{-3}$~yr$^{-1}$ \cite{LIGO_doc2016},
%\tcmag{and provides seeds for early supermassive BH formation.} 
\tcblue{The mechanism explains an avalanche of mysteries discovered  recently,} 
\tcred{may provide all or a large fraction of cosmological DM,}
\tcviol{and possibly a a lot of antimatter nearby in the Galaxy.}

\npni
\tcblue{This August announcement:}
"We report the discovery of a high proper motion, low-mass
white dwarf (LP 40-365) that 
\tcviol{travels at a velocity greater than the Galactic escape velocity}
\tccyan{and whose peculiar atmosphere is dominated by intermediate-mass elements."} 
S. Vennes et al,  Science, 2017, Vol. 357, p. 680; arXiv:1708.05568.\\
\tcmag{The origin is puzzling.}\\
\tcred{Can it be a compact primordial star?}

%\npni
\begin{figure}[tbp]
\begin{center}
\includegraphics[scale=0.7]{constraint_notes.pdf}
\caption{Constraints on PBH fraction in DM, $f=\rho_{\rm PBH}/\rho_{\rm DM}$,
where the PBH mass distribution is taken as
$\rho_{\rm PBH}(M)=M^2dN/dM$ %(see \cite{2016arXiv160706077C}).
The existing constraints (extragalactic $\gamma$-rays from evaporation (HR),
femtolensing of $\gamma$-ray bursts (F),
neutron-star capture constraints (NS-C), MACHO, EROS, OGLE microlensing (MACHO, EROS)
survival of star cluster in Eridanus II (E),
dynamical friction on halo objects (DF),
and accretion effects (WMAP, FIRAS))
%are taken from \cite{2016arXiv160706077C}
%and reference therein. 
The PBH distribution is shown for ADBD parameters $\mu=10^{-43}$~Mpc$^{-1}$,
$M_0=\gamma+0.1\times\gamma^2-0.2\times\gamma^3$ with $\gamma=0.75-1.1$ (red solid lines),
and $\gamma=0.6-0.9$ (blue solid lines).}
\label{f:PBH}
\end{center}
\end{figure}
%\npni
\begin{figure}[tbp]
\begin{center}
\includegraphics[scale=0.65]{bounds-text.pdf}
\end{center}
%\caption{Merging rate of binary BH (1/Gpc${^{3}}$/yr) per logarithmic mass interval over the universe age. The observed LIGO event rate is shown by the %purple rectangle.}
%\label{S1}
\end{figure}


\npni
\tcblue{Old predicitons and new data}\\[3mm]
\tccyan{Many things which were stated in our paper(s) a quarter century ago} 
\tcviol{and were badly criticized by those who payed attention to them}
\tcred{are now strongly supported by accumulated astronomical observations} 
and repeated  in many papers, \tcblue{naturally(?!), without a reference.}\\
\tcmag{I will briefly present our predictions,} 
\tcblue{review the recent astronomical data,
which now support our old statements,} 
\tcviol{and describe the theory.}


\npni
\tcblue{MYSTERIES IN THE SKY TODAY AND IN THE NEAREST PAST. } \\ [2mm]
\tccyan{ Every large galaxy %and some smaller ones 
contains a central supermassive BH with
mass  larger than} 
\tcred{ $\bm{ 10^{9}M_\odot}$} in giant elliptical
and compact lenticular galaxies
and \tcred{$\bm{\sim10^6 M_\odot}$} in spiral galaxies like Milky Way.\\
\tcred{The origin of these BHs is not understood.}
\tcviol{Accepted faith is that
these BHs are created by matter accretion to a central seed. }
\tcblue{But, the usual accretion efficiency is insufficient to create them during the Universe life-time,
14 Gyr.} \\
\tcmag{Even more puzzling: SMHBs  are observed  in small galaxies
 and even in almost \tccyan{EMPTY} space, where no material to make a SMBH can be found.}




\npni
\tcblue{The model, which explains all that, is based on the supersymmetric
(Affleck-Dine) scenario for baryogenesis}
\tcmag{modified by introduction of a general renormalizable coupling to the inflaton 
field, see below.}
%\tcblue{It was suggested  in 1993 (AD and J.Silk)} 
\tccyan{It is discussed in more details in several our papers} \tcred{applied to an
explanation of existence of the observed "old" objects in the young universe and
all mentioned above puzzles in the contemporary Universe.}\\
\tcviol{As a byproduct it may predict abundant antimatter objects in the Galaxy.}

\newpage
\noindent
%PART II \\
\tcblue{ Baryogenesis with SUSY condensate, Affleck and Dine (AD).} 
SUSY predicts existence of scalars with 
\tcred{${\bf B\neq 0}$.}
Such bosons may condense along \tcred{flat} directions of the quartic potential:
\be\tcblue{\bm{
U_\lambda(\chi) = \lambda |\chi|^4 \left( 1- \cos 4\theta \right),
}}\nonumber
\ee
and of the mass term, $\bm{ m^2 \chi^2 + m^{*\,2}\chi^{*\,2}}$:
\be\tcred{\bm{
U_m( \chi ) = m^2 |\chi|^2} {\left[\bm{ 1-\cos (2\theta+2\alpha)} 
\right],
}}\nonumber
\ee
where $\bm{ \chi = |\chi| \exp (i\theta)}$ and $\bm{ m=|m|e^\alpha}$.\\
\tcblue{If $\bm{\alpha \neq 0}$, C and CP are  broken.}\\
\tcred{In GUT SUSY baryonic number is naturally non-conserved} - non-invariance of $\bm{U(\chi)}$
w.r.t. phase rotation. 


\newpage
\noindent 
\tcmag{Initially (after inflation) $\bm{\chi}$ is away from origin and, when 
inflation is over, starts to evolve down to equilibrium point, $\bm{\chi =0}$,
according to Newtonian mechanics:}
\be\tcblue{\bm{
\ddot \chi +3H\dot \chi +U' (\chi) = 0.
}}\nonumber
\ee
Baryonic charge of $\chi$:
\be\tcred{\bm{
B_\chi =\dot\theta |\chi|^2
}}\nonumber
\ee
is analogous to mechanical angular momentum. 
${\bm{\chi}}$ decays transferred
baryonic charge to that of quarks in B-conserving process.
\tcred{AD baryogenesis could lead to baryon asymmetry of order of unity, much larger
than $\bm{10^{-9}}$.}


\newpage
\noindent
If ${\bf m\neq 0}$, the angular momentum, B, is generated by a different 
direction of the  quartic and quadratic valleys at low $\bm{\chi}$.
\tcred{If CP-odd phase $\bm{\alpha}$ is small but non-vanishing, both baryonic and 
antibaryonic regions are possible }
{\tcblue{with dominance of one of them.}\\
\tcred{Matter and antimatter domain may exist but globally ${\bf B\neq 0}$.}
 
 \newpage
\noindent
Affleck-Dine field $\bm \chi$ with CW potential coupled to inflaton $\bm \Phi$
(AD and Silk; AD, Kawasaki, Kevlishvili):
\be 
\tcblue{\bm{
U = \tcred{g|\chi|^2 (\Phi -\Phi_1)^2}  +
\lambda |\chi|^4 \,\ln( \frac{|\chi|^2 }{\sigma^2 })
}} 
\nonumber\\
\tcblue{\bm{+\lambda_1 \left(\chi^4 + h.c.\right) + %\nonumber\\
(m^2 \chi^2 + h.c.). \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,
}}\nonu
\ee
%CP would be broken, if the relative phase of $\bm{\lambda_1}$ and 
%$\bm m$ is non-zero, otherwise one can
%``phase rotate'' $\bm \chi$ and come to real coefficients. 
%{Coupling to fermions may break CP.}\\
\tcred{Coupling to inflaton is the general renormalizable one.}


\npni
If the window to flat direction, when $\bm{\Phi \approx \Phi_1}$ is open only \tcred{during 
a short period,} cosmologically small but possibly astronomically large 
bubbles with high ${\bm \beta}$ could be
created, occupying \tcblue{a small
fraction of the universe,} while the rest of the universe has normal
\tcblue{${\bm{ \beta \approx 6\cdot 10^{-10}}}$, created 
by small $\bm{\chi}$}. \\
\tcred{Phase transition of 3/2 order.}\\


\npni
\begin{figure}[htbp]
\begin{center}
\includegraphics[scale=0.55]{phi-evol.pdf}
%\caption
\end{center}
\end{figure}


\npni
\begin{figure}[htbp]
\begin{center}
\includegraphics[scale=0.55]{chi-rotate.pdf}
%\caption
\end{center}
\end{figure}

 
 \npni
This baryogenesis scenario could lead to an early formation of PBH or compact stellar-type objects and
 possibly (naturally?) to a comparable amount of anti-objects,
\tcred{such that the bulk of baryons and 
maybe antibaryons are contained in compact stellar-like objects or PBH,} 
\tcblue{plus the sub-dominant observed homogeneous baryonic background.}
{The amount of antimatter may be comparable or even larger 
than of KNOWN baryons,} 
\tcmag{but such ``compact'' (anti)baryonic objects
would not contradict  any existing observations.}\\ %(C.Bambi, AD  and S.I. Blinnikov, AD).
Bambi C., A.D., Nucl. Phys., B 784 (2007), 132;
A.D., Blinnikov S.I., Phys. Rev., D89 (1014), 2, 021301;
Blinnikov S.I., A.D., Postnov K.A., Phys. Rev., D92 (2015), 2, 023516;
 
 
\npni
\tcblue{SUMMARY}\\
%\npni
%\tcblue{Conclusion}\\
\tcred{1. A natural baryogenesis model leads to abundant fomation of PBHs and compact stellar-like
objects in the early universe after the QCD phase transition, $\bm{t \gtrsim 10^{-5}} $ sec.}\\
\tccyan{2. These objects have log-normal mass spectrum.} \\
\tcmag{3. PBHs formed at this scenario can explain the peculiar features of the sources
of GWs observed by LIGO.}\\

\npni
\tcviol{
 4. The considered mechanism solves the numerous mysteries of $\bm{z \sim 10}$ universe: abundant population
of supermassive black holes, 
early created \\
gamma-bursters and supernovae, early bright galaxies, and evolved chemistry including dust}.\\
%4. The considered mechanism solves the numerous mysteries of $\bm{z \sim 10}$ universe: SPBH, 
%early created gamma-bursters and supernovae, early bright galaxies, and evolved chemistry including dust}.\\
\tcred{5. There is persuasive data in favor of the inverted picture of galaxy formation, when first a supermassive 
BH seeds  are formed and later they accrete  matter forming galaxies.}\\
%Inverted picture of galaxy formation is advocated.}\\
\tccyan{6. An existence of supermassive black holes observed  in all large and some small galaxies and even in
almost empty environment is naturally explained.}\\
%SMBH observed  in almost empty environment is naturally explained.}\\

\npni
\tccyan{7. "Older than $\bm{t_U}$" stars may exist; the older age is mimicked by the unusual initial chemistry. }\\
\tcmag{8. Existence of high density invisible "stars" (machos) is understood.} \\
\tcviol{9. Explanation of origin of BHs with 2000 $\bm{M_\odot}$ in the core of globular cluster and the
observed density of GCs is presented}\\ 
\tcred{10. A noticeable fraction of dark matter or all of it can be made of PBHs.}\\

\npni
\tcblue{Conclusion}\\ 
\tcred{Large amount of astronomical data  very strongly demand abundant cosmological 
population of PBH with wide mass spectrum.} 
\tcviol{Such PBH nicely explain the mysteries accumulated during a few last years. }
%9. DM made of PBH.\\
 %\tcred{All the data strongly demand abundant cosmological population of PBH with wide mass spectrum.}
\\[3mm]
\tcblue{Testable predictions:}\\
\tccyan{A. Rate and masses of new GW events.} \\
\tcred{B. Possible existence of antimatter in our neighborhood, even in the Galaxy.}
\tcviol{C. PBH with $\bm{M = 2000-3000 \, M_\odot}$ in the cores of globular clusters.}\\
\tccyan{D. Number of PBH binaries as a function of mass, to be calculated.}

\npni
$$ $$
$$ $$
$$ \bm{
\tcblue{THE\,\,\,\, END }}
$$


%\end{document}


Among the problems of contemporary universe:
\tcblue{stars in the Milky Way, older than the Galaxy} and even 
\tcred{older than the universe} (within two sigma);\\
\tcblue{and distant high redshift ($\bm{ z = 5-10}$) population:} 
early galaxies, \tcred{QSO/SMBHs,} 
\tcblue{and  gamma-bursters.} Moreover, the young universe is full of  dust, which could not 
be created that early.


\newn
\npni
\tcblue{FACTS, quotations from publications:}
\tcred{Observed high-$\bf z$ objects which could not be created in so short time.}\\
There is a large "zoo" of astronomical objects formed  in surprisingly short times.
\tcblue{Several galaxies have been observed at high redshifts,
with natural gravitational lens ``telescopes,
e.g. a galaxy at \tcred{$\bm{z \approx 9.6}$} which was created when the universe was about
0.5 Gyr old,} (W. Zheng,  {\it  et al},
"A highly magnified candidate for a young galaxy seen when the Universe was 500 Myrs old"
arXiv:1204.2305).


\npni
An observation of not so young but extremely luminous galaxy was recently reported:
\tcblue{"The most luminous galaxies discovered by WISE"} 
Chao-Wei Tsai, P.R.M. Eisenhardt {\it et al}, \\
arXiv:1410.1751, 8 Apr 2015.\\
{\tcred{$\bm{L= 3\cdot 10^{14} L_\odot }$; age $\bm{\sim 1.3 }$ Gyr.}\\
%The new study outlines three reasons why the black holes in the ELIRGs could have grown so massive. First, they 
%may have been born big. In other words, 
{\tcblue{The galactic seeds, or embryonic black holes, might be bigger than thought possible.}
P. Eisenhardt: "How do you get an elephant?  One way is start with a baby elephant."
\tcred{The BH was already billions of $\bm{M_\odot}$ , when our universe was only a 
tenth of its present age of 13.8 billion years.}

\npni
According to F. Melia (1403.0908), "The Premature Formation of High Redshift Galaxies", 1403.0908:
\tcred{"Rapid emergence of high-z galaxies so soon after big bang} 
may actually be in conflict with 
current understanding of how they came to be. This
problem is very reminiscent of the better known (and
probably related) \tcred{premature appearance of supermassive
black holes at $\bm{z\sim 6}$.} It is difficult to understand how
\tcblue{$\bm{10^9 M_\odot}$} black holes
appeared so quickly after the big
bang \tcblue{without invoking non-standard accretion physics
and the formation of massive seeds,} 
\tcred{both of which are not seen in the local Universe."}


\npni
\tcblue{Another and even more striking example of early formed objects are high z quasars.}
A quasar with maximum \tcred{$\bm{ z = 7.085}$} has been observed i.e. it was 
formed earlier than \tcblue{$\bm{t  = 0.75}$ Gyr.} \\
Its luminosity and mass are: \\ 
\tcred{$\bm{L= 6.3 \cdot 10^{13} L_\odot}$} and
\tcred{$\bm{M=2 \cdot 10^9 M_\odot}$,}\\
D.J. Mortlock, {\it et al}, " A luminous quasar at a redshift of z = 7.085"
Nature 474 (2011) 616, arXiv:1106.6088 \\
\tcblue{The quasars are supposed to be supermassive black holes}
\tcred{and their formation in such short time by conventional mechanisms looks problematic.}

\newn
About 40 quasars with $\bm{z> 6}$ are already known, each quasar containing BH with %\\
$\bm{M \sim 10^9 M_\odot}$. 
\tcblue{Such black holes,
\tcred{when the Universe was less than one billion years old,} 
present substantial challenges to theories of the formation and growth of
black holes and the coevolution of black holes and galaxies.}\\



\npni
Very recently another monster was discovered
\tcred{"An ultraluminous quasar with a twelve billion solar mass black hole at redshift 6.30".}
Xue-BingWu et al,
%Feige Wang, Xiaohui Fan, Weimin Yi, Wenwen Zuo, Fuyan Bian, Linhua Jiang, Ian D. McGreer, Ran Wang,
%Jinyi Yang, Qian Yang, David Thompson & Yuri Beletsky
Nature 518, 512 (2015).\\
%\tcred{Now we have $\bf{ 10^{10} M_\odot}$ !!!}
\tcblue{There is already a serious problem with formation of lighter and less luminous quasars}
\tcred{which is multifold deepened with this new "creature".}
\tcred{The new one with $\bm{M \approx 10^{10} M_\odot }$  makes the formation}
\tcblue{absolutely impossible in the standard approach.}

\npni
\tcblue{The medium around the observed early quasars contains
considerable amount of ``metals''} (elements heavier than He). 
According to the standard picture, only elements up to $\bm{^4}$He  { and traces of Li, Be, B}
were formed by BBN, \tcblue{while heavier elements were created
by stellar nucleosynthesis and} \tcred{dispersed in the interstellar space by supernova explosions.}
%Later molecular dust must form.

\npni
\tcred{The universe at $\bm{z >6}$ is quite dusty,}
D.L. Clements et al "Dusty Galaxies at the Highest Redshifts",
%Authors: David L Clements, Josh Greenslade, Dominik A. Riechers, Julie Wardlow,
 %Ismael Perez-Fournon, The HerMES Red Collective, The HerMES & H-ATLAS Consortia
1505.01841.\\
% We show that the use of red colour as the basis for selecting candidate high
%redshift dusty galaxies from surveys made with Herschel has proved highly successful. 
\tcblue{The highest redshift such object, HFLS3, lies at z=6.34 and
numerous other sources have been found.}\\
L. Mattsson, "The sudden appearance of dust in the early Universe",1505.04758:
\tcred{Dusty galaxies show up at redshifts corresponding
to a Universe which is only about 500 Myr old.}

\npni
\tcblue{Hence, prior to or simultaneously with the QSO formation a rapid star formation should take place.}
\tcred{These stars should evolve to a large number of
%could produce plenty of 
supernovae enriching interstellar space by metals through their explosions} which later make molecules and dust.\\
\tcblue{(We all are dust from SN explosions, but probably at much later time.)} \\
%[3mm]
Another possibility is a non-standard BBN due to very high baryonic density, which allows for formation of heavy elements 
beyond lithium.

\npni
%\newn
Observations of high redshift gamma ray bursters (GBR) also indicate 
\tcblue{a high abundance of supernova at large redshifts.} 
\tcred{The highest redshift of the observed GBR is 9.4} and there are a few more
GBRs with smaller but still high redshifts. 
\tcblue{The necessary star formation rate for explanation of these early
GBRs is at odds with the canonical star formation theory.}

\npni
\tcblue{"Back to the future".}\\
\tcred{"Quasar quartet embedded in giant nebula reveals rare massive structure in distant universe",}
J.F. Hennawi et al, Science 15 May 2015, 348  p. 779, \\
\tcblue{discovered in a survey for Lyman-Е’В± emission at redshift  $\bm{z \approx 2}$.}\\
%we discovered a physical association of four quasars embedded in a giant nebula. }
%All galaxies once passed through a hyperluminous quasar phase powered by accretion onto a 
%supermassive black hole. But because these episodes are brief, 
{\tcred{Quasars are rare objects separated by cosmological distances, so
the chance of finding a quadruple quasar is $\bm{\sim 10^{-7}}$.} 
It implies that the most massive structures in the distant universe have a tremendous supply 
($\bm{\sim 10^{11} M_\odot}$) of cool dense ($\bm{ n \approx 1/}$cm$\bm{^3}$) gas,
\tcred{in conflict with current cosmological simulations.}

\newn
Present days:
\tcblue{it seems that
every large galaxy and some smaller 
ones contain a central supermassive BH} whose
masses  are larger than 
\tcred{ $\bm{ 10^{9}M_\odot}$} in giant elliptical
and compact lenticular galaxies
and \tcred{$\bm{\sim10^6 M_\odot}$} in spiral galaxies like Milky Way.
\tcred{The origin of these  superheavy BHs is not understood.}

\newn
\tcblue{The mass of BH is typically 0.1\% of the mass of the stellar bulge of galaxy} 
% \cite{BH-bulge,*SaniMarconi}
but some galaxies may  have huge BH: \tcred{e.g. NGC 1277  has
the central BH  of  $\bm{1.7 \times 10^{10} M_\odot}$, or $\bm{60}$\% of its bulge mass.}
%\cite{NGC1277}.
\tcblue{This fact creates serious problems for the
standard scenario of formation of central supermassive BHs by accretion of matter in the central 
part of a galaxy.}
\tcred{An inverted picture looks more plausible, when first a supermassive black hole was formed and 
attracted matter serving as seed for subsequent galaxy formation.}\\
Bosch et al, Nature 491 (2012) 729;
AD, J. Silk, 1974; AD, M. Kawasaki, N. Kevlishvili, 2008. 

\newn
\tcblue{More examples:}
F. Khan, et al
%K. Holley-Bockelmann,  P. Berczik 
arXiv:1405.6425.\\
Although supermassive black holes\\ 
correlate well with their host
galaxies, there is an emerging view that outliers exist.
\tcblue{ Henize 2-10, NGC 4889,
and NGC1277 are examples of SMBHs at least an order of magnitude more massive
than their host galaxy suggests. }
\tcred{The dynamical effects of such ultramassive central black holes is unclear. }


\newn
\tcblue{A recent discovery of an ultra-compact dwarf galaxy
older than 10 Gyr, enriched with metals, and probably with a massive black in its center} 
\tcred{seems to be at odds with the standard model}
J. Strader,  {\it et al} %A. C. Seth, D. A. Forbes, G. Fab- biano, A. J. Romanowsky, J. P. Brodie, C. Conroy, 
%N. Caldwell,  V. Pota, C. Usher, and J. A. Arnold, 
 Astrophys. J. Lett. 775, L6 (2013), arXiv:1307.7707. \\
\tcblue{The dynamical mass is $\bm{2\times 10^8 M_\odot}$ 
and  $\bm{R \sim 24}$ pc -}  \tcred{very high density.}\\
Chandra: variable central X-ray source with \tcred{ $\bm{L_X \sim 10^{38}}$ erg/s,} which may be
\tcblue{an AGN associated with a massive black hole} or a low-mass X-ray binary.

\npni
\tcblue{"An evolutionary missing link? A modest-mass early-type
galaxy hosting an over-sized nuclear black hole",}
J. Th. van Loon, A.E. Sansom,
Xiv:1508.00698v1 [astro-ph.GA] 4 Aug 2015.\\ 
\tcred{BH mass, $\bm{M_{BH} = (3.5 \pm 0.8) \cdot 10^8 M_\odot}$,}
\tcblue{host galaxy $\bm{M_{stars} = 2.5^{+2.5}_{-1.2} \cdot 10^{10} M_\odot}$,}
and accretion luminosity: \\
\tcred{$\bm{ L_{AGN} = (5.3 \pm 0.4) \cdot 10^{45} }$erg/s $\bm{\approx 10^{12} L_\odot}$.}\\
%(12\% of the Eddington luminosity). 
\tcblue{The AGN is more prominent than expected for a host galaxy
of this modest size.} The data are in tension with the accepted picture in which
this galaxy would recently have transformed from a star-forming disc galaxy into an
early-type, passively evolving galaxy.


\newn
\tcblue{Old stars in the Milky Way:}\\[3mm]
Employing thorium and uranium % abundances
in comparison with each other and with several stable elements \tcblue{the age of
metal-poor, halo star BD+17$^o$ 3248 was estimated as}  \tcred{ $\bm{13.8\pm 4}$ Gyr.}\\
% "The chemical composition and age of the metal-poor halo star BD+17$^o$ 3248"
J.J. Cowan, C. Sneden, S. Burles, {\it et al}
Ap.J. 572 (2002) 861, astro-ph/0202429. \\[3mm]
\tcblue{The age of inner halo of the Galaxy} \tcred{$\bm{11.4\pm 0.7}$ Gyr,} J. Kalirai, 
"The Age of the Milky Way Inner Halo"
Nature 486 (2012) 90, arXiv:1205.6802.

\newn
\tcred{The age of a star in the galactic halo, HE 1523-0901, was estimated to be 
about 13.2 Gyr.}
\tcblue{First time many different chronometers, such as the U/Th, U/Ir, Th/Eu and Th/Os ratios to
measure the star age have been employed.}\\[3mm]
"Discovery of HE 1523-0901: A Strongly r-Process Enhanced Metal-Poor Star with Detected Uranium",
A. Frebe, N. Christlieb, J.E. Norris, C. Thom  Astrophys.J. 660 (2007) L117;
astro-ph/0703414. 

\newn
Metal deficient \tcblue{high velocity} subgiant in the solar neighborhood
HD 140283  has the age \tcred{$\bm{14.46 \pm 0.31 }$ Gyr.}\\
H. E. Bond, E. P. Nelan, D. A. VandenBerg, G. H. Schaefer,  D. Harmer, Astrophys. J. Lett. 765, L12 (2013), arXiv:1302.3180.\\
\tcred{The central value exceeds the universe age by two standard deviations,\\ 
if $\bm{H= 67.3}$ and $\bm{t_U =13.8}$; }\\
\tcblue{if $\bm{H= 74}$, then $\bm{ t_U = 12.5}$.} \\

\npni
X. Dumusque, {\it et al}
\tcblue{"The Kepler-10 Planetary System Revisited by \\
HARPS-N: A Hot Rocky World and a Solid Neptune-Mass Planet".}\\
arXiv:1405.7881; Ap J., 789, 154, (2014).
\tcred{Very old planet, $\bm{10.6^{+1.5}_{-1.3} }$ Gyr.}\\
\tcblue{(Age of the Earth: 4.54 Gyr.)} \\
\tcred{A SN explosion must must precede  formation of this planet.}



\npni
\tcblue{Summary:}
%\tcred{Recent cosmological puzzles.}\\
\Huge{{\bf
\tcred{many objects in the universe were formed much earlier than 
allowed by the standard theory.}\\
Among them:
\tcblue{stars in the Milky Way, older than the Galaxy} and even 
\tcred{older than the universe} (within two sigma);\\
\tcblue{distant high redshift ($\bm{ z\sim 10}$) staff:} 
galaxies, \tcred{QSO/supermassive BHs,}\\ 
supernovae, \tcblue{ gamma-bursters,} evolved chemistry and a lot of dust.\\
\tcred{The universe is much more developed at early times than it was expected.}\\[3mm]

\npni
\tcblue{More misteries:}
\tcred{It was found that the BH masses are concentrated in the narrow range
$\bm{ (7.8 \pm 1.2) M_\odot }$} (1006.2834)\\
This result agrees with another paper where
\tcblue{a peak around $\bm{8M_\odot}$, a paucity of sources with masses below
 $\bm{5M_\odot}$, and a sharp drop-off above
$\bm{10M_\odot}$ are observed,} arXiv:1205.1805.
\tcred{These features are not explained in the standard model.}

\npni
\tcblue{A simple and natural (?) model can explain all that and more,} \tcred{e.g. mysterious MACHO's,}
quite strange, unexpected, mass distribution of BHs in the Galaxy
\tcred{and predict abundant cosmological antimatter in our neighborhood, i.e. in the Galaxy and its halo.}  \\
\tcblue{However, it is unclear, if the CDM-problems mentioned at the beginning can be solved, provided galaxies
are formed around earlier created seeds. }
\\[5mm]


END OF PART I.
%%%DSP
%\npni 
%\tcblue{Prevailing point of view at the present time: }
%\tcred{all the universe is made only of matter and there is
%no primeval antimatter.}

%\npni
%\tcblue{Still the fact that antimatter exists 
%created fundamental cosmological\\ puzzle:} 
%\tcred{why the observed universe is 100\% dominated by 
%matter?}\\
%Antimatter exists but not antiworlds, why?
%\tcblue{The problem deepened because of approximate 
%symmetry between particles and antiparticles.}\\
%In fact before 1956, the common faith in exact 
%C, P, and T symmetries looked unbreakable.\\

%dsp

\npni
PART III \\[3mm]
\tcblue{The puzzle of the observed predominance of matter over antimatter 
was resolved by} \tcred{Sakharov, (1967) on the basis of the conditions:}\\
\tcblue{I. Nonconservation of baryons.} \\
\tcred{II. Violation of symmetry between particles and antiparticles, 
i.e. C and CP.} \\
III. Breaking of thermal equilibrium.\\[3mm]
\tcblue{(None of these three conditions is obligatory.)}\\

\npni
\tcblue{Plethora of baryogenesis scenarios\\ 
which can explain one number:}
\be \tcred{\bm{
\beta_{observed} = \frac{N_B-N_{\bar B}}{N_\gamma} 
\approx 6\times 10^{-10}\,.
}}\nonumber
\ee
\tcblue{The usual outcome: $\bm{ \beta = const}$, }
{which makes it impossible to distinguish between models and} 
\tcred{does not leave space for cosmological antimatter.}\\
NB: all the models, but one (Affleck and Dine) give rise to a small
$\bm{ \beta}$ but \tcblue{AD may create $\bm{\beta \sim 1}$.}
  

\npni
\tcred{ Natural generalizations of the simplest
models of baryogenesis allow for a lot of
antimatter almost at hand.}\\
\tcblue{An observation of cosmic antimatter will give a clue
to baryogenesis, to the mechanism of cosmological
C and CP breaking, and present an extra argument in  
favor of inflation.}\\
Since generalized scenarios predict a whole function
\tcred{$\bm{\beta (x)}$,} the models are falsifiable.


\npni
\tcblue{Maybe there are already data indicating to antimatter in the universe and even in the Galaxy.}\\
\tcred{"Something is rotten in the state of \st{Denmark} the Universe"} (almost quote of Marcellus from "Hamlet") \\
\tcblue{There is an avalanche of  observed early formed objects which could not be created in so young universe.}
Their existence can be explained in the model which predicts a lot of real antimatter.


%%%%%%%%%%%%%%%%%%%%


\newpage
\noindent
\tcblue{ Baryogenesis with SUSY condensate, Affleck and Dine (AD).} 
SUSY predicts existence of scalars with 
\tcred{${\bf B\neq 0}$.}
Such bosons may condense along \tcred{flat} directions of the quartic potential:
\be\tcblue{\bm{
U_\lambda(\chi) = \lambda |\chi|^4 \left( 1- \cos 4\theta \right),
}}\nonumber
\ee
and of the mass term, $\bm{ m^2 \chi^2 + m^{*\,2}\chi^{*\,2}}$:
\be\tcred{\bm{
U_m( \chi ) = m^2 |\chi|^2} {\left[\bm{ 1-\cos (2\theta+2\alpha)} 
\right],
}}\nonumber
\ee
where $\bm{ \chi = |\chi| \exp (i\theta)}$ and $\bm{ m=|m|e^\alpha}$.\\
\tcblue{If $\bm{\alpha \neq 0}$, C and CP are  broken.}\\
\tcred{In GUT SUSY baryonic number is naturally non-conserved} - non-invariance of $\bm{U(\chi)}$
w.r.t. phase rotation. 


\newpage
\noindent 
Initially (after inflation) $\bm{\chi}$ is away from origin and when 
inflation is over starts to evolve down to equilibrium point, $\bm{\chi =0}$,
according to Newtonian mechanics:
\be\tcblue{\bm{
\ddot \chi +3H\dot \chi +U' (\chi) = 0.
}}\nonumber
\ee
Baryonic charge of $\chi$:
\be\tcred{\bm{
B_\chi =\dot\theta |\chi|^2
}}\nonumber
\ee
is analogous to mechanical angular momentum. 
${\bm{\chi}}$ decays transferred
baryonic charge to that of quarks in B-conserving process.
\tcred{AD baryogenesis could lead to baryon asymmetry of order of unity, much larger
than $\bm{10^{-9}}$.}


\newpage
\noindent
If ${\bf m\neq 0}$, the angular momentum, B, is generated by a different 
direction of the  quartic and quadratic valleys at low $\bm{\chi}$.
\tcred{If CP-odd phase $\bm{\alpha}$ is small but non-vanishing, both baryonic and 
antibaryonic regions are possible }
{\tcblue{with dominance of one of them.}\\
\tcred{Matter and antimatter domain may exist but globally ${\bf B\neq 0}$.}
 
\newn
\tcblue{A minor modification of AD-scenario can lead to very early formation of compact stellar-type objects and
naturally to a comparable amount of antiobjects,}
\tcred{such that the bulk of baryons and 
(equal) antibaryons
are in the form of compact stellar-like objects or PBH,} 
\tcblue{plus sub-dominant observed homogeneous baryonic background,}
{the amount of antimatter may be comparable or even larger 
than of KNOWN baryons,} but such ``compact'' (anti)baryonic objects
would not contradict  any existing observations.

%BBN and CMB and even make (some?) DM.  
\newpage
\noindent
Affleck-Dine field $\bm \chi$ with CW potential coupled to inflaton $\bm \Phi$
(AD and Silk; AD, Kawasaki, Kevlishvili):
\be 
\tcblue{\bm{
U = \tcred{g|\chi|^2 (\Phi -\Phi_1)^2}  +
\lambda |\chi|^4 \,\ln( \frac{|\chi|^2 }{\sigma^2 })
}} 
\nonumber\\
\tcblue{\bm{+\lambda_1 \left(\chi^4 + h.c.\right) + %\nonumber\\
(m^2 \chi^2 + h.c.). \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,
}}\nonu
\ee
%CP would be broken, if the relative phase of $\bm{\lambda_1}$ and 
%$\bm m$ is non-zero, otherwise one can
%``phase rotate'' $\bm \chi$ and come to real coefficients. 
%{Coupling to fermions may break CP.}\\
\tcred{Coupling to inflaton is the general renormalizable one.}


\npni
GREAT EXPECTATIONS:\\
\tcred{Both a simple} \tcblue{and probably
unique,} \tcred{generalization of the theory, and 
available astronomical data
allow for a lot of antimatter just ``next door''.}\\
\tcblue{Maybe Dirac and Schuster were right saying that antiworlds exist!?}\\
\tcred{NB: interesting  
anti-objects should be astronomically large, so inflation is
necessary} \tcblue{ and not too large to avoid problems with
existing observations.} 

\npni
If the window to flat direction, when $\bm{\Phi \approx \Phi_1}$ is open only \tcred{during 
a short period,} cosmologically small but possibly astronomically large 
bubbles with high ${\bm \beta}$ could be
created, occupying \tcblue{a small
fraction of the universe,} while the rest of the universe has normal
\tcblue{${\bm{ \beta \approx 6\cdot 10^{-10}}}$, created 
by small $\bm{\chi}$}. \\
\tcred{Phase transition of 3/2 order.}


\npni
The distributions of high baryon density bubbles over length 
and mass have log-normal form:
\be
\tcred{\bm{ 
\frac{dN}{dM} = \mu^2 \exp{[-\gamma \ln^2 (M/M_0)]}
}}
\nonumber
\label{dn-dM}
\ee
where $\bm{\mu}$, $\bm{\gamma}$, and $\bm{M_0}$ are constant parameters.\\
\tcblue{Spectrum is practically model independent, it is determined by inflation.} 


\npni
INHOMOGENEITIES.\\[3mm]
\tcred{1. After formation of domains with large $\bm{\chi}$
due to different equations of state inside and outside of the
domains:}  some nonrelativistic matter inside the bubbles and 
relativistic outside.\\
\tcred{2. Second period of $\bm{\delta\rho}$ generation
after the QCD phase transition } 
\tcblue{ at ${\bf T\sim 100}$ MeV when quarks made
non-relativistic protons.}
BH masses from
a few $\bm{M_\odot}$ to $\bm{10^{6-7} M_\odot}$. \\
\tcblue{Compact objects (not BH) with smaller masses could be formed too.}



\newpage
\noindent
FAVORABLE FEATURES\\
\tcblue{
On the tail of the distribution very heavy BH may be created, 
$\bm{ \sim 10^7 M_\odot}$.}\\
\tcred{A mechanism of early quasar formation with evolved chemistry} - one of 
the mysteries of the standard model.\\
\tcblue{Superheavy PBH are seeds for structure formation!?}\\
At the moment there is no satisfactory mechanism for formation of the 
observed superheavy BH.\\
\tcblue{An explantation of high-redshift SN, gamma-bursters, stars older than 
the universe \tcred{ (observed in the Milky Way),...}}
Cut-off BH distribution at $\bm{\sim 6M_\odot}$.

\newn
The log-normal mass distribution  naturally explains some features 
of stellar mass black holes in the Galaxy.
\tcred{It was found that their masses are concentrated in the narrow range\\
$\bm{ (7.8 \pm 1.2) M_\odot }$} (1006.2834)\\
This result agrees with another paper where
\tcblue{a peak around $\bm{8M_\odot}$, a paucity of sources with masses below
 $\bm{5M_\odot}$, and a sharp drop-off above
$\bm{10M_\odot}$ are observed,} arXiv:1205.1805.
\tcred{These features are not explained in the standard model.}

\newn
A modifications of $\bm{U_{int}}$ leads to a more 
interesting spectrum of the early formed stellar type objects,
e.g.,  if:
\be
\tcred{\bm{
U_{\rm int}  = {\lambda_1 |\chi|^2 } 
 \left( \Phi - \Phi_1\right)^2   \left( \Phi - \Phi_2\right)^2 ,
%\label{U-int-2}
}}\nonumber
\ee
\tcblue{we come to a two-peak mass distribution of the PBHs and compact stars,} which is 
probably observed, 
%see papers~\cite{BH-masses-1,BH-masses-2,*FarrSravan}  and the references therein, 
but not explained up to now.\\ 
ArXive: 1011.1459: \tcblue{"sample of black hole masses provides strong evidence of a gap between the maximum neutron star mass and the lower bound on black hole masses"} - maybe lower mass BH are created by a normal mechanism of stellar collapse.


\newpage
\noindent
Impact on BBN.\\[2mm]
\tcred{If $\bm{\beta \equiv \eta \gg 10^{-9} }$, light (anti)element 
abundances would be
anomalous: much less anti-deuterium, more anti-helium.}
%\be\tcblue{\bm{
%T_{BBN} = \frac{65\,\,keV}{1- 0.03\,ln\, \eta_{10}}
%}\nonu
%}\ee
%where ${\bm{ \eta_{10} = 10^{10} n_B /n_\gamma}}$.\\
\tcblue{Look for clouds with anomalous chemistry.} However,
with 50\% probability it may be  
the normal matter with anomalous $\bm{ n_B /n_\gamma}$.\\
%baryon-to-photon ratio.}  \\
\tcred{If such a cloud or compact object is found, search for
annihilation there.}

\newn
\tcblue{Evolved chemistry in the so early formed QSOs can be explained, at least to some extend,}
\tcred{by more efficient production of metals during BBN due to much larger ratio 
$\bm{\beta =N_B/ N_\gamma}$. }
The standard BBN essentially stops at $\bm{^4}$He due to very
small $\bm{\beta}$. However, in the model considered here \tcblue{$\bm{\beta}$ is
much larger than the canonical value, even being close or exceeding unity.}\\
On the other hand, early formed stellar type objects \tcred{could make abundant  supernovae 
and create metals and dust.}

\npni
\tcblue{The suggested mechanism leads to creation of compact stellar-like
objects and \tcred{equal number of compact anti-objects} 
in the early universe at\\ 
$\bm{ t= 0.01- 1}$ sec.}\\
\tcred{So the universe may be full of early formed and by now dead or low luminosity stars
(and antistars).}\\
Natural explanation of MACHOS(??) - invisible stellar mass objects observed by gravitational 
micorlensing; too many for usual stars.


\newn
\tcblue{Summary:}\\ 
{\tcred{1. Compact anti-objects mostly survived in the early universe,
especially if they are PBHs.} \\
\tcblue{2. A kind of early dense stars might be formed with 
initial pressure outside 
larger than that inside.}\\
\tcred{3. Such ``stars'' may evolve quickly and, in
particular, make early SNs,\\ enrich the universe with heavy\\ 
(anti)nuclei and reionize the universe.} 

\newpage
\noindent
\tcblue{4. Early formation of superheavy BHs, i.e. QSO with enriched chemistry.}\\
\tcred{5. Energy release from stellar like objects in the early
universe is small compared to CMBR.}\\
6. Not dangerous for BBN since the volume of B-bubbles is small.
\vs{0.3cm}\\
\tcblue{One can always hide any undesirable objects into black holes.}



\npni
$$$$
$$$$
\\[10mm]
\begin{center}
\tcblue{THE END}
\end{center}

\end{document}

\npni
\tcred{2. Novel mechanism of astrophysical objects creation in the early universe:}\\ 
AD, J. Silk, \tcblue{ Baryon isocurvature fluctuations at small scales and baryonic dark matter ",}
PRD 47 (1993) 4244;\\
AD, S.Blinnikov,
\tcblue{"Stars and Black Holes from the very Early Universe"},  
PRD 89 (2014) 021301. \\
\tcblue{It is based on the SUSY baryogenesis (Affleck-Dine)} 
\tcred{and predicts as a by-product abundant cosmological antimatter even in the Galaxy.}
\tcblue{Spectrum of primordial perturbations at small (astrophysical) scales is much different from 
flat inflationary spectrum.}


\npni
PART II \\[3mm]
Primordial antimatter in the universe and its search and bounds.\\
\tcred{Antiparticles are predicted and observed in experiment,}
\tcblue{but it is unknown if antimatter, i.e. antistars, antiplanets, antigalaxies exist  anywhere in the universe.}  \\
{\tcred{Presently cosmological antimatter (the real one not just antiparticles)
is actively searched for  by several groups;} more  sensitive detectors are
proposed for future observations.
%- \tcred{burst of recent activity.}

\npni
\Huge{{\bf
%\tcred{86 years ago, one of the most impressive physics discoveries 
%of XX century was made:} 
\tcblue{P.A.M. Dirac,} Proc. Royal Soc. London, A117 (1928) 610, 
\tcblue{predicted 
``with the tip of his pen'' a whole world of antimatter}
(not just a small planet). \tcred{ He assumed initially that positively charged "electron" was proton!?} 
\tcblue{Critics by Oppenheimer: hydrogen instability (if proton is a hole in negative continuum), }
\tcred{forced Dirac to conclude that "anti-electron" is a NEW particle with the same mass as $\bm{e^-}$ (1931).}
At that time a hypothesis about a new particle was not as blameless as today.
%\\[3mm]

\npni
\tcred{Carl Anderson, discovery of positron, 1933;} 
Nobel prize in 1936. \tcblue{According to the Anderson  words: it was not difficult, simply nobody looked for that.} \\[3mm]
\tcred{Dirac's Nobel prize in 1933 immediately after the
experiment.}

\npni
\tcblue{ Paul A.M. Dirac:
``Theory of electrons and positrons'',
Nobel Lecture, December 12, 1933:} 
\tcred{``It is quite possible that...
these stars being built up mainly of positrons 
and negative protons.
In fact, there \tcblue{may be half the stars of each kind.} 
The two kinds of stars would both show exactly the same spectra, 
and} \tcblue{there would be no way
of distinguishing them by present astronomical methods.''}\\

\npni
{\tcblue{ It seems that now we know ways to distinguish stars from a antistars by observations 
from the Earth.}\\
\tcred{The spectra are not exactly the same,} \tcblue{even if CPT is unbroken} and polarization of radiation
could be a good indicator or the type of emitted neutrinos/antineutrinos from supernovae.

\npni
\tcred{Dirac was the second person to talk about antimatter.}
\tcblue{ In 1898,
30 years before Dirac and one year after discovery
of electron (J.J. Thomson, 1897)
\tcred{Arthur Schuster} (another British physicist) conjectured that 
there might be other sign electricity, ANTIMATTER, and 
supposed that}
\tcred{ there might be 
entire solar systems, made of antimatter,} 
\tcblue{INDISTINGUISHABLE  from ours.}

\npni
\tcred{Schuster's wild guess: matter and antimatter are 
capable to annihilate and produce VAST 
energy.} \\
\tcblue{He believed that they were gravitationally 
repulsive having negative mass.} Two such objects on close contact
should have vanishing mass!?

\npni
A. Schuster, Nature, 58 (1898) 367. 
\tcred{Potential Matter. Holiday Dream.}\\
\tcblue{``When the year's work is over and all sense of responsibility has 
left us, who has not occasionally set his fancy free to dream about 
the unknown, perhaps the unknowable?''}\\
\tcred{"Astronomy, the oldest and yet most
juvenile of the sciences, may still have some surprises in
store. May antimatter be commended to its case".}

%dsp

\npni
\tcred{ Astronomical search for antistars.}\\
%\tcred{Possibility of astronomical observations of antistars.} 
\tcblue{If CPT is broken and $\bm{\Delta m \neq 0}$, 
spectra of anti-atoms might be different in irregular way, not described by a redshift.} However, CPT may be broken
but masses remain equal.\\
\tcred{Still, with CPT or without it, there are chances for distant observation of antiworlds.}

\npni
\tcred{If CPT is respected:}\\
\tcblue{Atomic spectra with broken C and CP} (AD, Khriplovich, Rudenko). \\
The positions of levels of atoms and antiatoms are probably the same, but partial decay
widths are different. \tcblue{Unfortunately, for hydrogen the effect is tiny
(accidental cancelation?): }
\be \tcred{\bm{
\Delta \Gamma /\Gamma \sim 10^{-28}.
}}\nonumber
\ee
\tcblue{An amplification, in particular, in heavier atoms and in external magnetic or electric fields might be possible.}

\npni
\tcblue{ Some other ways to see an antistar} (AD, Novikov, Vysotsky).
\tcred{Through communication with inhabitants: }
it is usually supposed that to this purpose CP-violation is to be used.
\tcblue{If the light charged leptons in the shells of their atoms
are more frequently produced in $\bm{K_L}$ decays $\bm{K_L \to \pi^\pm e^\mp \nu}$,
then we communicate with  anti-people.}


\npni
\tcblue{Polarized radiowaves can be used in the communication asking}  \tcred{if 
the polarization of charged lepton emitted in neutron $\bm{\beta}$ decay is the same?}\\
\tcblue{CP-violation is not necessary, breaking of P is enough.}\\
However, the stellar system may be non-inhabited and even if  it is,  this process would
take an extremely long time and is more proper for a science fiction.
\tcred{We need to find methods independent on intelligent life in the system under scrutiny.}

\npni
\tcblue{Neutrinos versus antineutrinos produced by thermonuclear reactions in a star.} However,
the fluxes are too low for the present day sensitivity.  \tcred{Neutrinos from SN explosions have better chance to be 
registered.}
At the first stage of SN explosion \tcblue{neutrinos} from the neutronization reaction 
$\bm{pe^- \rar n\nu}$ are emitted and \tcred{antineutrinos} from anti-SN.

%(Let us note that spin-flavour conversion
%of Majorana neutrinos would mimic $\overline{SN}$ explosion \cite{Ah}. However the spectra of the detected 
%antineutrinos should be different in this case and in the case we consider).

\npni
\tcblue{ Detection of anti-stars by photons produced in weak interaction processes.} 
\tcred{These photons are longitudinally polarized and their energy can be well defined if they are
created in two body decays.}  Mono-energetic photons produced e.g. in 
$\bm{B\rar K^\star\gamma}$ should be left-handed because of dominance of 
$\bm{b\rar s\gamma}$ penguin transition with left-handed $\bm{s}$-quark.\\
\tcred{However, one can hardly imagine noticeable abundance of B-mesons in stars,}
\tcblue{and most probably there is an equal amount of  $\bm{B}$ and $\bf{\bar B}$
mesons.}

\npni
\tcred{Stars with abundant strange quarks look more promising.} 
 \tcblue{The outer shell of such stars is populated by $\bm{\Sigma}$-hyperons and 
the polarization of photons emitted in $\bm{\Sigma^+ \rar p\gamma}$ decay could indicate
if the photons are emitted by hyperon or anti-hyperon.}
The polarization is large, \tcred{$\bm{\alpha = -0.76\pm 0.08}$} and the branching ratio is nonnegligible
\tcred{$\bm{(1.23 \pm 0.05)\times 10^{-3}}$.} 

\npni
Circular polarization of photons in the $\bm{\gamma}$-transitions of nuclei was observed
in the terrestrial experiments:\\
\tcred{$\bm{P_\gamma = (4\pm 1) \cdot 10^{-5}}$ in $\bm{^{175} Lu}$ transition with the emission of 395 keV photon,} \\
\tcblue{\bm{$P_\gamma = -(6 \pm 1) \cdot 10^{-6}}$ for 482 keV photon emitted in $\bm{^{181}Ta}$ transition,}\\ 
\tcred{$\bm{P_\gamma = (1.9 \pm 0.3) \cdot 10^{-5}}$
for 1290 keV photon emitted in transition of $\bm{^{41}K}$.}
\tcblue{Measurement of circular polarization of such photon lines is ideally suited for search of antistars.}


\npni
\tcblue{Traditional ways to search for cosmic antimatter.}\\
%Two more types of observational data:}\\
Indirect: astronomical manifestations of antimatter:
0.5 MeV or 100 MeV gamma-rays, distortion of CMB, 
impact on BBN and LSS formation.\\
\tcred{Direct: registration of antimatter which cannot be secondary 
produced, mainly cosmic anti-nuclei, and anomalous antiprotons and
positrons in cosmic rays.}\\
\tcblue{Nowadays, burst of experimental activity for  
direct search of cosmic antimatter:}

\npni
Existing missions for the direct search: \\
\tcred{1. BESS: Japanese Balloon Borne Experiment with Superconducting\\ 
Solenoidal Spectrometer.} \\
\tcblue{2. PAMELA (Italian-Russian space mission): Payload for Antimatter 
Matter Exploration and Light-nuclei Astrophysics.}\\
3. AMS: AntiMatter Spectrometer (Alpha Magnetic Spectrometer),
CERN-MIT-NASA.

\npni
\tcred{Planned missions:}\\[3mm]
\tcblue{PEBS (Positron Electron Balloon Spectrometer,)
search for cosmic positrons and antiprotons.}\\[2mm]
GAPS (Gaseous Antiparticle Spectrometer), search for
X-rays from de-excitation of exotic atoms, 
\tcred{may reach 2 orders of magnitude better sensitivity 
than AMS for $\bm{\bar He /He}$. }

\npni
{Search for cosmic anti-helium, existing bounds:}\\[5mm]
\tcblue{BESS:}
\tcred{$\bm{\bar He / He < 3\times 10^{-7}}$.}\\[3mm]
Expected:\\
\tcblue{PAMELA:}
\tcred{ $\bm{{\bar He}/{ He} < 3\times 10^{-8}}$;}\\
\tcblue{AMS-2:}
\tcred{ $\bm{\bar He / He < 10^{-9}}$.}\\[3mm]
\tcblue{Observed flux of cosmic helium at \\
$\bm{ E< 10}$ GeV/nuclei:}\\
$ \bm{\tcred{ dN/dE = 10^{2} /m^2/str/sec/GeV.}}$


\npni
\tcblue{Expected secondary produced anti-nuclei:}\\[3mm]
Anti-deuterium is produced in $\bm{\bar p\, p}$
or $\bm{\bar p\, He}$ collisions (Duperray et al, 2005)
The predicted flux of anti-deuterium:\\ 
$\tcred{\bm{\sim 10^{-7} /m^{2}/ s^{-1} /sr/(GeV/n)},}$\\
i.e. 5 orders of magnitude lower than the observed
flux of antiprotons.\\
\tcblue{The expected fluxes of secondary produced 
$\bm{^3\bar He}$ and $\bm{^4\bar He}$ 
are respectively 4 and
8 orders of magnitude smaller than the flux of anti-D.}

\npni
\tcblue{Observations and bounds, summary.}\\[3mm]
\tcred{$\bm{ \bar p / p \sim 10^{-5}-10^{-4}}$, observed, can
be explained by secondary production;}\\
$\bm{He/p \sim 0.1}$;\\
\tcblue{Upper limit: $\bm{\bar He / He < 3\times 10^{-7}}$};\\
Theoretical predictions: $\bm{ \bar d \sim 10^{-5} \bar p}$,\\
$\bm{ ^3\bar He  \sim 10^{-9} \bar p}$,
$\bm{ ^4\bar He \sim 10^{-13} \bar p}$.\\
\tcblue{From the upper limit on $\bm{\bar{He}}$: the nearest
single antigalaxy should be further than} 
\tcred{10 Mpc (very crudely).}

\npni
\tcblue{Search for antinuclei at LHC.}\\
According to the data of ALICE detector, %obtained at LHC, 
production of an antinucleous
\tcred{with an additional antinucleon is suppressed only by factor about 1/300} which is much milder than
the suppression factors presented above. Probably the difference is related to much higher energies at
which data of ALICE are taken. 
\tcblue{The events with such energies are quite rare in cosmic rays.}

\npni
\tcblue{From cosmic gamma rays:}\\[2mm]
Nearest \tcred{anti-galaxy} could not be closer 
than \tcred{at $\sim$10 Mpc} (Steigman, 1976),
from annihilation with $\bm{p}$ in common intergalactic cloud.\\
\tcblue{Fraction of antimatter Bullet Cluster} 
\tcred{$\bm{ < 3\times 10^{-6}}$}
(Steigman, 2008).\\[4mm]
\tcblue{CMB excludes LARGE isocurvature fluctuations at $\bm{ d> 10}$ Mpc.}\\
\tcred{BBN excludes large ``chemistry'' fluctuations at $\bm{ d> 1}$ Mpc.}

\npni
\tcblue{Review: P.v. Ballmoos, arXiv:1401.7258}
Bondi accretion of interstellar gas to the surface of an antistar:
\be \tcred{\bm{
 L_\gamma \sim 3\cdot 10^{35} (M/M_{\odot})^2 v_6^{-3}
}} \nonumber
\ee
put  a limit \tcblue{$\bm{N_{\bar *} / N_{*} <  4\cdot 10^{-5} }$} inside 150 pc from the Sun. \\
\tcblue{The presented bounds are true if antimatter makes the 
same type objects as the OBSERVED matter.}\\
\tcred{For example, compact faster objects made of antimatter may be abundant
in the Galaxy but still
escape observations (discussed below).}\\[3mm]
END OF PART II




\newpage
\noindent
\tcblue{
ANTIMATTER TODAY}
\vs{0.5cm}\\
Democratic guiding principle: \\
\tcblue{forget theory,}\\
\tcred{anything not forbidden is allowed.}

\newpage
\noindent
\tcblue{EVOLUTION IN THE EARLY\\ UNIVERSE,} C. Bambi, AD (2007).\vs{0.3cm}\\
Bubbles with ${\bm{ {\delta\rho}/{\rho}<1}}$ but with
$$\tcred{\bm{M_B>M_{Jeans}}} $$
\tcblue{(gravity crashes matter against pressure)}
at horizon \tcred{would decouple from cosmological expansion} and
form compact stellar type objects or lower density clouds.\\
\tcblue{Could such anti-objects survive against early annihilation?} 



\newpage
\noindent
\tcblue{THE ANTI-CREATION MECHANISM}\\
AD, J. Silk (1993); AD, M. Kawasaki, N. Kevlishvili (2008). \vs{0.4cm}\\
\tcblue{Affleck-Dine baryogenesis: SUSY condensate of a
scalar baryonic field $\bm{ \chi}$ along}
\tcred{flat directions of the potential.} \\
\tcblue{Normally it predicts very high}\\
\tcred{$\bm {\beta = n_B/n_\gamma\sim 1}$} and theoretical 
efforts are needed to 
diminish it.


\npni
\tcblue{``Rotation'' of $\bm \chi$ is transformed into baryonic number of
quarks by \\
\tcred{B-conserving decays of  $\bm \chi$,}} producing small homogeneous
background baryon asymmetry, to this end an explicit CP-violation is necessary,
and \tcred{little bubbles with huge baryonic
number density.}



\npni
\tcblue{Flat directions: 
$\bm{\cos (4\theta) = 0}$,} $\bm{\chi = |\chi|e^{i\theta}}$,\\
if mass term is negligible w.r.t. to $\bm{\lambda_1}$-interaction.\\ 
\tcred{Two last (red) terms are not $\bm{U(1)}$ invariant
and break B-conservation.}
$\bm{J_\mu^{(B)} = i\chi^\dagger \partial_\mu \chi + h.c. },$\\
\tcblue{$\bm{B = J_t^{(B)}}$ is the angular momentum.}


\npni
\tcblue{An incomplete ``shopping list'' of the baryogenesis (BG) 
scenarios includes} (IV and V are favorable for anti-creation):
\\[3mm]
\tcred{I. Heavy particle decays (Sakharov)}\\
{II. Electroweak BG (Kuzmin, Rubakov, Shaposhnikov)}.\\
%Too weak in MSM but may work with TeV gravity.\\
\tcblue{III. Baryo-through-leptogenesis (Fukugita, Yanagita).}\\
\tcred{IV. SUSY condensate BG (Affleck, Dine).}\\
\tcblue{V. Spontaneous BG (Cohen, Kaplan).}\\

\npni
\tcred{VI. BG by evaporation of primordial black holes (Zeldovich, AD)}.\\
VII. Space separation of baryons and antibaryons.
(Omn{\'e}s, and later, into higher dimensions)
or compact\\ (anti)quark nuggets. \\
\tcblue{VIII. BG due to CPT violation (Zeldovich, AD) }.\\
IX. Baryogenesis and darkogenesis.\\
\tcblue{X. BG by topological defects.}

\npni
\tcblue{C and CP violation in cosmology.}\\
Both are discovered and confirmed by \\
\tcred{direct experiment} but the mechanism realized in
cosmology may have nothing to do with that realized in particle
physics.  \\
\tcblue{What about Occam's razor: entities must not be multiplied 
beyond necessity (``entia non sunt multiplicanda praeter necessitatem''). }


%%%%

\newpage
\noindent
\tcblue{Three possibilities to break CP :} \vspace{0.5cm}\\
\tcred{1. Explicit}, the usual one in particle physics. Normally leads
to the universe without antimatter. \vspace{0.3cm}\\
\tcblue{2. Spontaneous,} locally indistinguishable from explicit, but leading
to globally charge symmetric universe.\vspace{0.3cm}\\
\tcred{3. Stochastic or dynamical,}\\ 
unobservable in particle physics. May lead to noticeable amount of 
antimatter and globally asymmetric universe.


\newpage
\noindent
\tcred{I. Explicit CP- breaking.} Complex constants in 
Lagrangian, in particular (in MSM), complex 
Yukawa couplings transformed by the
Higgs field $\bm{ \langle \phi \rangle \neq 0}$ into  
a non-vanishing phase in CKM-mixing matrix. 
However, in MSM the baryon asymmetry 
is \tcred{too small,} \tcblue{by 10 orders of magnitude.}\\
\tcred{New physics beyond MSM is necessary.}


\newpage
\noindent
\tcred{II. Spontaneous CP-violation,  (T.D. Lee, 1974). } A complex scalar field $\bm{\Phi}$ 
acquiring different vacuum expectation values:
\be\tcblue{\bm{
\langle \Phi \rangle = \pm f\,.
}}\nonumber
\ee
Lagrangian is CP-invariant.\\
\tcred{Locally indistinguishable from explicit but
leads to globally charged symmetric universe,}
\tcblue{ 50:50 matter and antimatter.}

\npni
\tcred{PROBLEMS:}\\
\tcblue{1. Domain wall problem,} (Zel'dovich, Kobzarev, Okun):
\tcred{huge surface energy density of walls between domains
with different signs of CP-breaking amplitude destroys isotropy
of the universe.}
\tcblue{To avoid that the nearest domain of antimatter should be at
${\bf l_B \gg }$ Gpc} or a mechanism of wall destruction is
necessary.

\npni
\tcblue{2. The size of domains are too small and matter and antimatter
annihilate leaving behind an empty universe.}
\tcred{Can be solved with mild inflationary expansion after CP-breaking took
place (Sato, 1980).} 
\tcblue{Still many problems: domain wall extinction, suppression of
powerful annihilation, etc...}\\
\tcblue{Observational bound on spontaneous CP-violation
from gamma-ray background:}
\tcred{$\bm{ l_B >}$ Gpc} (Cohen, De Rujula, Glashow, 1996).


\npni
\tcblue{III. Dynamical or stochastic \\
CP-violation (AD, 1992),} 
realized by a complex scalar field displaced from 
the equilibrium point due to infrared instability 
of light scalars at DS (inflationary) stage, 
\tcred{$\bm{ \chi^2 \sim H^3 t}$,} \tcblue{(sign ?)} 
and relaxed to the equilibrium point after baryogenesis.\\
\tcblue{It could operate only in the early universe and disappeared 
without trace today.}
\tcred{No domain wall problem.}\\

\npni
\tcred{Why do we multiply entities against Occam?  }
Nature is usually very economical.
\tcblue{However, this  mechanism is quite natural because it always operate 
in the early universe if there exists
any complex scalar field with $\bm{m<H_{inf}}$.}\\
Such temporary CP-violation could give rise to an 
inhomogeneous baryon 
asymmetry, $\bm{ \beta(x)}$, with \tcred{antimatter nearby.}



\newn
\tcblue{Phenomenology and bounds on compact antimatter objects and disperse anti-clouds}
(Bambi, AD, 2007;\\  Blinnkov, AD, Postnov, 2015) \\
{Possible astronomical objects:}\\
\tcblue{1. Gas clouds of antimatter.}\\
\tcred{2. Isolated antistars.}\\
\tcblue{3. Anti stellar clusters.}\\
4. Anti black holes.\\
\tcblue{5. Stellar wind.}\\
\tcred{5. Antimeteorites.}\\
{6. What else?}
%\vs{0.7cm}\\

\newpage
\noindent
WHERE:\vs{0.2cm}\\
\tcblue{Inside galaxies or outside galaxies?}\\
\tcred{Inside galactic halos or in intergalactic space?}\vs{0.3cm}\\
Consider all the options.\\
\tcred{New part:} \tcblue{ unusual compact objects, e.g. dead or half dead 
(anti)stars,\\
(anti)BH with (anti)atmosphere.}

\newpage
\noindent
\tcblue{OBSERVATIONAL SIGNATURES
%Observational signatures.
}\vs{0.3cm}\\
\tcred{1. Gamma background.}\\
\tcblue{2. Excessive antiprotons.}\\
3. Positrons.\\
\tcred{4. Antinuclei.}\\
\tcblue{5. Compact sources of $\bm{\gamma}$ radiation.}\\
6. Catastrophic phenomena.\\
\tcred{7. Rapid change of stellar luminosity.}

\npni
\tcred{Two types of objects (clouds and compact stars):}\\
\tcblue{1. Gas clouds, mean free path of protons 
${\bm{ l_p}}$ is larger than the size of the (anti)cloud.
\tcred{Annihilation proceeds in whole volume.}}\\
Low density or small clouds would not survive in a galaxy. They would 
disappear during 
\be\tcred{
{\bm{ \tau =  10^{15} \,\, sec\,\, 
\left(\frac{10^{-15}cm^3/s}{\sigma_{ann} v}\right)\,
\left(\frac{cm^{-3}}{n_p}\right),}
\nonu}}
\ee
may survive in the halo.


\npni
The luminosity for \tcred{volume annihilation:}
\be\tcblue{\bm{
L_\gamma^{(vol)} 
%\approx 0.3 L_{tot}^{(vol)} 
\approx
 10^{35}\,{\rm \frac{erg}{s}}\, 
%\left( \frac{\sigma_{ann}v}{10^{-15}\,{\rm cm^3/s}}\right)
 \left(\frac{R_B}{0.1\,{\rm pc}}\right)^3}} \nonumber\\
 \tcblue{\bm{\left( \frac{n_p}{{\rm 10^{-4}\,cm}^{-3}}\right)}}
 %\nonumber\\
\tcblue{\bm{ \left(\frac{n_{\bar p}}{10^4 {\rm cm}^{-3}}\right). 
}}\label{L-gamma-vol2}
\nonumber
\ee
\vspace{0.3cm}\\
Flux on the Earth at d=10 kpc: \\
\tcred{$\bm{10^{-7}\gamma/{\rm s/cm}^2 }$} or 
\tcblue{$\bm{10^{-5}{\rm MeV/\,s/cm}^2 }$ },
to be compared with cosmic background 
\tcblue{$\bm{10^{-3}/{\rm MeV/s/cm}^2 }$,} 
\tcred{pointlike sources.}


\newpage
\noindent
\tcblue{2. Compact objects, ${\bm{  l_{free}\ll l_s}}$,}
\tcred{surface annihilation, much less efficient.}
\tcblue{Total luminosity, 
${\bm{ L = 2m_p \cdot 4\pi\,l_s^2\,n_p v }}$:}
\be\tcred{{\bm{
L_{tot} 
\approx 10^{27}\,\frac{erg}{sec}\,
\left(\frac{n_p}{cm^3}\right)\left(\frac{l_s}{l_\odot}\right)^2 .
}\nonu
}}\ee
Fraction into gamma-rays is about\\ 
20-30\%.\\
\tcred{Unidentified EGRET sources, from \\
clouds or compact objects?}


\newpage
\noindent
\tcblue{Stellar wind:}
\be{\bm{
\dot M = 10^{12} W\,g/sec
}}\nonu
\ee
where $\bm{ W=\dot M /\dot M_{\odot}}$.\\
\tcblue{If all ``windy'' particles annihilate, the luminosity
per star:} 
$$\tcred{{\bm{ L= 10^{33} W \,\,{\rm erg/sec.} }}}$$
%For $\bm{n_p =1/{\rm cm}^3}$ and 
%$\bm{v_p = 10^{-3}}$ the effective size of the
%sphere where annihilation takes place is about $\bm{10^{14}}$ cm.
Mean free path of $\bm{\bar p}$ in the galaxy is about $\bm{10^{23}}$ cm
(depending on their velocity). \tcred{Gamma luminosity of the Galaxy:}
$\tcblue{\bm{\
L_\gamma \approx 10^{33}\bar N W\,erg/s\,.}} $


\newpage
\noindent
\tcred{Number density of antinuclei is bounded by the density of
\tcblue{``unexplained'' ${\bf \bar p}$} and the fraction of antinuclei in
stellar wind with respect to antiprotons.} \\
It may be the same as in
the Sun but if antistars are old and evolved, this number must be much 
smaller.\\
\tcblue{On the other hand, the relative amount of anti-nuclei could be
larger because of explosions of the early SN.}

\newpage
\noindent
\tcblue{Heavy antinuclei from anti-SN} may be abundant but their
ratio to ${\bf \bar p}$ can hardly exceed the same for normal SN.\\
\tcred{Explosion of anti-SN would create a large cloud of antimatter, which
should quickly annihilate producing vast energy - a spectacular event.}\\
\tcblue{However, most probably such stars are already dead and SN might
explode only in very early galaxies or even before them.}


\npni
\tcblue{COSMIC POSITRONS.}\\[4mm]
Gravitational proton capture by an (anti)star is more probable 
than capture of electrons, due to larger mobility of $\bf{p}$.
\tcred{Antistar is neutralized by forced positron ejection. }\\
\tcblue{It would be most efficient in galactic center where 
$\bm{n_p}$ is large.}\\ 
\tcred{0.511 MeV line (observed) must
be accompanied by wide spectrum $\bm {\sim 100}$ MeV radiation.} \\
Also: Schwinger process at Schwarzschild horizon.


\npni
\tcblue{EXOTIC EVENTS}\vspace{0.3cm}\\
\tcred{Similar mass star-antistar collision,\\ 
$\bm \gamma$-bursters} (???):
\be \tcblue{\bm{
\Delta E \sim 10^{48}\,erg\, \left(\frac{M}{M_\odot}\right)
\left(\frac{v}{10^{-3}}\right)^2
}}\nonumber
\ee
Annihilation pressure pushes the stars apart.  
Collision time $\bm {\sim 1}$ sec. \\
\tcblue{Radiation is emitted in the narrow disk but not jet.}

\npni
\tcblue{Collision with \tcred{RED GIANT:} 
compact antistar travels inside creating 
an additional energy source. Change of color and luminosity(?).}\\
\tcred{$\bm{\Delta E_{tot} \sim 10^{38}}$ erg and $\bm{\Delta t \sim }$ month.} 
\\[4mm]
\tcblue{Transfer of material in binary system} - 
\tcred{hypernova  explosion!? }

\newpage
\noindent
\tcblue{OBSERVATIONAL BOUNDS.}\\[3mm]
I. Stellar wind:
\be\tcred{\bf{
N_{\bar S} / N_S \leq 10^{-6} W^{-1},
}}
\nonumber
\ee
\tcblue{from the total galactic luminosity in 100 MeV photons, 
$\bm{ L_\gamma = 10^{39} erg/s}$ and from the flux of the positron 
annihilation line
$\bm{ F \sim 3\cdot 10^{-3}/cm^2/s}$.}\\
$\bm {W\ll 1}$  is natural to expect because the primordial antistars 
may be already evolved.


\newpage
\noindent
\tcblue{II. Antihelium-helium ratio:}
\be\tcred{\bm{
N_{\bar S} / N_S  = (\bar{He}/He) \leq 10^{-7},
}}
\nonumber
\ee
if the antistars are similar to the usual stars, though most probably not.



\newpage
\noindent
\tcblue{CONCLUSION}\vs{0.4cm}\\
\tcred{1. The Galaxy may possess a noticeable amount of antimatter.}\\
2. Theoretical predictions are vague and model dependent, but testable
and may permit to distinguish between scenarios of BG.\\
\tcblue{3. Not only ${\bf ^4 \bar{He}}$ is worth to look for but 
also heavier anti-elements. Their abundances should be similar 
to those observed in
SN explosions.} 

\newpage
\noindent
\tcred{4. Regions with an anomalous abundances of light elements are suspicious
that there may be anti-elements.}\\
\tcblue{5. A search of cosmic antimatter has nonvanishing chance to be 
successful.}
6. Dark matter made of BH, anti-BH, and dead stars is a promising
candidate. There is a chance to understand why ${\bf \Omega_B =0.05}$ is 
similar to ${\bf \Omega_{DM} = 0.25}$.\\

\newpage
\noindent
\tcred{7. Detection of $ {\bm \bar \nu}$ in the first burst from anti-SN
explosion.}\\[2mm]
\tcblue{8. Measurement of polarization of\\  electromagnetic radiation (?).}\\
{9. Existing signatures in favor:}\\
\tcred{May the observed positron 0.511 MeV line from the galactic bulge
\tcblue{and especially (if confirmed) from the halo}
be a signature of cosmic antimatter!?}\\
\tcblue{Unidentified EGRET sources.}




\npni
\npni
\begin{figure}
	\centering
%\vspace{4cm}
	%\hspace*{-7cm}
	\hspace{-5cm}
	\includegraphics[scale=1.2]{ChiModEvol.eps}
	%	\caption{Evolution of $\bm {|\chi|}$ in the bubble}
	\label{fig:ChiModevol}
\nonumber
\end{figure}
{Evolution of $\bm {|\chi|}$ in the bubble. The phase is chaotic.}


\npni
\begin{figure}[t]
\begin{center}
\leavevmode
%\vskip 0.2truecm
%\epsfxsize=3.4truein \epsfbox{neutrino_1.eps}
%\epsfxsize=5.7truein \epsfbox{fig3_nu2000.eps}
%\epsfxsize=5.7truein \epsfbox{Chi2.eps}
\epsfxsize=7.0truein \epsfbox{Chi2.eps}
\end{center}
\end{figure}
``Rotation'' of $\bm \chi$ due to non-sphericity of the potential
and creation of $\bm{B \neq 0}$.

\npni
\begin{figure}[t]
\begin{center}
\leavevmode
%\epsfxsize=7.0truein \epsfbox{Potevolution.eps}
\epsfxsize=7.0truein \epsfbox{Potevolution.eps}
\end{center}
\end{figure}
\noindent
Evolution of the potential of $\bm \chi$ as a function of the
inflaton field $\bm \Phi$.

\npni
\tcblue{Experimental tests of CPT are mostly based on measurements of mass differences of particles and 
antiparticles. In particular:}
\be \bm{\tcred{
\frac{\Delta m_e }{m_e} = \frac{m_{e^+} - m_{e^-}} { m_{e}} < 8\times 10^{-9}.  
}}\nonumber
\ee
Hence $\bm{\Delta m_e < 4\cdot 10^{-3}}$ eV.\\[2mm]
\tcblue{If $\bm{\Delta m_e \neq 0}$, then the photon mass must be non-zero }(AD+V.Novikov):
\begin{equation} \tcred{\bm{
m_\gamma^2 \sim \left(\frac{\alpha}{\pi}\right) \Delta m^2  \lesssim
3\cdot 10^{-8}  \,\,{\rm eV}^2 \,.
}}\nonumber
\end{equation}
Another way around: \tcblue{$\bm{\Delta m_e \sim 20 m_\gamma}$.}

\npni
\tcred{Bounds on $\bm{m_\gamma}$:}\\
The Earth based experiments give\\ % for the Compton wave length of the photon
\tcblue{$\bm{\lambda_C > 8\cdot 10^{7}}$ cm,} i.e. $\bm{m_\gamma < 3\cdot 10^{-13}} $ eV, and
respectively
\tcred{$\bm{\Delta m < 6 \cdot 10^{-12} }$~eV.}\\
%nine orders of magnitude stronger than (\ref{Delta-m}).
Magnetic field of the Jupiter implies
%it follows that the Compton wave length of photon is larger than
\tcblue{$\bm{\lambda_C >5\cdot 10^{10}}$ cm} or $\bm{m_\gamma <  4\cdot 10^{-16} }$ eV, and
respectively \tcred{$\bm{\Delta m < 8 \cdot 10^{-15} }$~eV.}\\
The strongest solar system bound comes from the analysis of the solar wind
extended to the Pluto orbit: \\
\tcblue{$\bm{\lambda_C > 2\cdot 10^{13}}$~cm.} 
% i.e. $m_\gamma <  10^{-18} $ eV. This is an
%"official" limit present by the Particle Data Group~\cite{1}. The corresponding bound on the
%electron-positron mass difference is 
 \tcred{ So $\bm{\Delta m < 2 \cdot 10^{-17} }$~eV.} 
%which is almost 14 orders of magnitude stronger than the direct bound on $\Delta m$.

\npni
The strongest existing bound follows from the  observation of  large scale magnetic fields
in galaxies(Chibisov): \\
\tcblue{$\bm{\lambda_C > 10^{22}}$~cm} and respectively\\
%$m_\gamma < 2 \cdot 10^{-27} $ eV. Correspondingly 
\tcred{ $\bm{\Delta m < 4 \cdot 10^{-26} }$ eV,} 23 orders of magnitude stronger
than the direct bound. \\ %limit on $\bm{\Delta m_e}$.\\
%the electron-positron mass difference.\\
\tcblue{Similar bounds should be valid for any charged particle mass differences, in
particular, for the  quark mass difference.} \tcred{It would inhibit  baryogenesis 
in scenarios with mass differences, } \tcblue{but other ones due to a
possible change of kinetics 
remain feasible.}

\npni
\tcblue{CPT-odd models with $\bm{\Delta m \neq 0}$ are pathological and there are examples
of CPT-violation with $\bm{\Delta m = 0}$ and unbroken Lorenz symmetry} (Chaichian, AD, Novikov, Tureanu)
\tcred{ - a countereexample to Greenberg theorem. }
\\[4mm]
\tcblue{Non-conservation of energy-momentum tensor, if $\bm{\Delta m \neq 0}$,  and problems with massless 
graviton.}

%%%%%%%%%%%%%%%%%%%%

%\npni 
%\tcblue{Prevailing point of view at the present time: }
%\tcred{all the universe is made only of matter and there is
%no primeval antimatter.}

%\npni
%\tcblue{Still the fact that antimatter exists 
%created fundamental cosmological\\ puzzle:} 
%\tcred{why the observed universe is 100\% dominated by 
%matter?}\\
%Antimatter exists but not antiworlds, why?
%\tcblue{The problem deepened because of approximate 
%symmetry between particles and antiparticles.}\\
%In fact before 1956, the common faith in exact 
%C, P, and T symmetries looked unbreakable.\\

%dsp



\npni
\tcblue{Century old questions:}\\ [2mm]
\tcred{Whether antiworlds, antistars or similar astronomically
large pieces of antimatter may exist in the universe?}\\
\tcblue{What are observational bounds on existence of antimatter
in the universe and in the Galaxy?}\\
\tcred{Do theory and observations allow for significant amount of
antimatter in our neighborhood?}\\
If antimatter exists, is it natural to expect that there are antiworlds?


\npni
{Two roads in investigating matter-\\
antimatter similarity and distinction:}\\
\tcblue{1. On  earth: theory and experiments on C, CP, and CPT breaking, e.g. 
particle and antiparticle decays or e.g. study of anti-hydrogen properties.}\\
 \tcred{2. In the sky: cosmology and astrophysics; mechanisms of baryogenesis leading to 
 antiworlds and manifestations of primordial antimatter.}

\npni
\tcred{It is established in experiment that particles and antiparticles are different, so that C (1956) and CP (1964)
 invariances are broken,} \\
while most probably CPT remains intact:
\tcblue{CPT-theorem: a local Lorenz invariant theory with canonical spin-statistics relation is invariant
w.r.t to CPT-transformation.}

\npni
Still, everything is  questioned in physics, including all sacred principles. \tcred{"If God does not exist everything is allowed",}
Dostoevsky, "Karamazov brothers".\\
\tcred{Without principles predictive power of theory will be lost.}  \\
\tcblue{With broken CPT spectra of matter and antimatter might be different, but not necessarily so.}

\npni
CPT-invariance demands: 
\be \tcred{\bm{ 
m= \bar m\,\,\,\, {\rm and}\,\,\, \Gamma_{tot} = \bar\Gamma,
}}\nonumber
\ee
\tcblue{but, partial decay rates of  charge conjugated channels 
and analogous cross-sections of separate charge conjugated processes may be and
are different.} Total cross-section of charge conjugated reactions may also be different (due to difference of
in- and out-  multi-body states).
 \tcred{These distinctions, despite CPT, make  life possible! }




\npni
TO REMEMBER:

Connection of DM and baryons:

arXiv:1008.1997
Date: Wed, 11 Aug 2010 20:16:23 GMT   (76kb,D)

Title: Darkogenesis
Authors: Jessie Shelton, Kathryn M. Zurek
Categories: hep-ph
Comments: 20 pages, 2 figures
Report-no: MCTP-10-28
\\
 In standard models of baryogenesis and of dark matter, the mechanisms which
generate the densities in both sectors are unrelated to each other. In this
paper we explore models which generate the baryon asymmetry through the dark
matter sector, simultaneously relating the baryon asymmetry to the dark matter
density. In the class of models we explore, a dark matter asymmetry is
generated in the hidden sector through a first order phase transition. Within
the hidden sector, it is easy to achieve a sufficiently strong first order
phase transition and large enough $CP $ violation to generate the observed
asymmetry. This can happen above or below the electroweak phase transition, but
in both cases significantly before the dark matter becomes non-relativistic. We
study examples where the Asymmetric Dark Matter density is then transferred to
the baryons both through perturbative and non-perturbative communication
mechanisms, and show that in both cases cosmological constraints are satisfied
while a sufficient baryon asymmetry can be generated.
\\ ( http://arxiv.org/abs/1008.1997 ,  76kb)
------------------------------------------------------------------------------
\npni
See new papers in the net about BG - in my list

Asymmetric dark matter and the Sun.
Mads T. Frandsen, Subir Sarkar, (Oxford U., Theor. Phys.) . Mar 2010. (Published Jul 2, 2010). 4pp.
Published in Phys.Rev.Lett.105:011301,2010.
e-Print: arXiv:1003.4505 
---------------------
arXiv:1008.2399 (*cross-listing*)
Date: Fri, 13 Aug 2010 22:34:22 GMT   (44kb)

Title: Hylogenesis: A Unified Origin for Baryonic Visible Matter and
 Antibaryonic Dark Matter
Authors: Hooman Davoudiasl, David E. Morrissey, Kris Sigurdson, Sean Tulin
Categories: hep-ph astro-ph.CO
Comments: 5 pages, 2 figures
\\
 We present a novel mechanism for generating both the baryon and dark matter
densities of the Universe. A new Dirac fermion X carrying a conserved baryon
number charge couples to the Standard Model quarks as well as a GeV-scale
hidden sector. CP-violating out-of-equilibrium decays of X, produced in
low-temperature reheating, sequester antibaryon number in the hidden sector,
thereby leaving a baryon excess in the visible sector. The antibaryonic hidden
states are stable dark matter. A spectacular signature of this mechanism is the
baryon-destroying inelastic scattering of dark matter that can annihilate
baryons at appreciable rates relevant for nucleon decay searches.
\\ ( http://arxiv.org/abs/1008.2399 ,  44kb)
---------------------------------------------------
arXiv:1008.2487
Date: Sun, 15 Aug 2010 01:30:06 GMT   (6kb)

Title: Baryogenesis from Dark Sector
Authors: N. Haba and S. Matsumoto
Categories: hep-ph
Comments: 6 pages
\\
 We propose a novel mechanism for generating the suitable baryon asymmetry
through a dark (hidden) sector. This is a Baryogenesis through a reverse  
pathway of ``asymmetric dark matter'' scenario. At first, dark matter asymmetry
is generated in the early universe, and the asymmetry is then transferred into
the suitable baryon asymmetry in the standard model sector. This mechanism
allows us not only to realize the generation of the baryon asymmetry but also
to give a correct amount of dark matter density simultaneously within a simple
framework.
\\ ( http://arxiv.org/abs/1008.2487 ,  6kb)
------------------------------------------------------

\npni
\npni
\Huge{{\bf
\tcblue{Content of the lectures:}\\
\tcred{1. Introduction.}\\
\tcblue{2. Search for cosmic antimatter.}\\
3. General features of baryogenesis. \\
\tcblue{4. CP-violation in cosmology.}\\
\tcred{5. Models of baryogenesis.} \\
\tcblue{6. Mechanisms of creation of cosmological antimatter.}\\
\tcred{7. Observational manifestations of\\ 
(abundant) antimatter.}\\
8. Perspectives and conclusion. 

\npni
\npni
\tcblue{Now let's discuss three Sakharov's conditions.}\\[3mm]
\tcred{I. Non-conservation of baryonic number, B.}\\ 
The weakest point when Sakharov proposed the mechanism.
\tcblue{It was believed that baryons last forever,} as 
``a diamond-and-safire bracelet'' (from Anita Loos's 
``Gentlemen Prefer Blondes'').\\
The motto was: \tcred{``we exist ergo baryons are conserved''.}

\npni
\tcblue{Today situation is opposite: theory predicts nonconservation
of B} \tcred{and cosmology presents an ``experimental\\
proof of that.}\\
Now: \tcblue{``we exist ergo baryons are not conserved''}
the same fact (our existence) but opposite conclusion. Sometimes
theory helps to understanding the world.

\newpage
\noindent
\tcblue{Proof of nonconservation of baryons comes from inflation.}
Cosmological inflation is practically 
\tcred{an experimental fact:}\\
\tcblue{1. Flatness, ${\bf \Omega =1}$.} Without inflation the adjustment 
should be at ${\bf 10^{-60}}$.\\
\tcred{2. Homogeneity, isotropy, horizon -} all solved.\\
\tcblue{3. Small primordial perturbations at astro-scales with 
almost FLAT spectrum,} \tcred{OBSERVED.}\\

\npni
An observation of gravitational waves will eliminate all 
existing skepticism, but their absence will not kill inflation. \\[4mm]
\tcblue{Inflation is the only known way
to create the observed, suitable for life universe universe.}\\
\tcred{However, beware of danger of 
no-go theorems in physics, e.g. SUSY.}

\npni
Sufficient inflation \\
\tcred{($\bm{\sim}$ 70 Hubble times)} \\
could proceed only if the energy \\
density is approximately \tcblue{constant}.
\be
\bm{\tcblue{
H=\dot a /a \sim \sqrt {\rho}/m_{Pl}
}}\nonumber
\ee
and ${\bf a \sim exp ( Ht)}$ if $\bm{ H= const}$.
\vspace{0.5cm}\\
If baryons are conserved, 
the energy density associated 
with baryonic charge (\tcblue{baryonic number})
cannot be
constant and inflation could last at most\\ 
\tcred{4-5 Hubble times.}

\newpage
\noindent
If baryonic charge were conserved:
\be
\bm{\tcred{
B\sim 1/a^3, \,\,\, \rho_B \sim 1/a^n,}\,\, n=3-4
}
\nonumber
\ee
At RD-stage $\bm{ \rho_B \approx 10^{-7}\rho_{tot} }$ and
\be
\bm{\tcblue{
\rho_B/\rho_{tot} \approx const }}
\nonumber
\ee
till inflation, backward in time.
At inflation $\tcred{\bm{ \rho_{tot}= const}}$
(without baryons),\\ 
while $\tcblue{\bm{ \rho_B \sim exp (-4Ht)}}$.\\
For $\bm{ Ht >4-5}$: sub-dominant baryons became dominant,
\tcblue{$\bm{ \rho_{tot} \approx \rho_B}$} and 
\be
\tcred{\bm{
\rho \neq const  
}}\nonumber
\ee

\npni
\tcblue{B-nonconservation, theory.}\\[3mm]
\tcred{1. B is classically conserved in the minimal standard 
electroweak theory, but this conservation is broken due to
quantum corrections - chiral anomaly} ('t Hooft, 1974).\\
\tcblue{The non-conservation is tiny at $\bm{T=0}$ but may be 
strongly enhanced at high temperatures:}
\be\tcred{\bm{
\Gamma(0) \sim  m^4_W\,e^{ - {4\pi }/{\alpha_W}} \sim 10^{-170}\,,}}
\nn \\
\tcblue{\bm{
\Gamma(T) \sim \alpha^{4-5} T^4\,,\, \,\,  T>TeV\,. 
}}\nn
\ee

\npni
\tcblue{2. Grand unified theories (GUT): } quarks and leptons are
in the same multiplet, so naturally transformed into each
other, \tcred{$\bm{\Delta B \neq 0}$:}
\be \tcblue{\bm{
\Gamma \sim M_{GUT}^{-4}\,.
}}\nn
\ee
\tcred{3. Many extended theories, e.g. SUSY, where 
all operators with $\bm{\Delta B \neq 0}$ are allowed.}

\npni
\tcblue{No direct experimental confirmation of B-nonconservation,
only upper bounds.}
Proton life-time:
\be\tcred{\bm{
\tau_p > 10^{30}-10^{33} \,\,\,} {\bf years
}}\nn
\ee
In some theories proton is stable but neutron may transform into
antineutron:
\be \tcblue{\bm{
\tau_{n \bar n} > 10^8\,s.
}}\nn
\ee

\npni
\tcblue{Gravitational interactions do not conserve baryonic number.}
\tcred{Gravity breaks all global symmetries.}
Gravitational proton decay through virtual black hole
(Zeldovich, 1976). Three quarks in proton form a BH which evaporates
e.g. into $\bm{e^+ \pi^0}$:
\be \tcred{\bm{
\tau_p = m_{Pl}^4/m_p^5 \sim 10^{45} }\, {\bf years\,.
}}\nn
\ee
\tcblue{Effect is negligible but maybe observable in TeV gravity
with $\bm{m_{Pl} \sim }$ TeV. Life-time diminishes by
64 orders of magnitude. } See, however, below.

\newpage
\noindent
\tcblue{Why CP-breaking is necessary but C-breaking is not enough?}\\
\tcgold{A formal answer:}\\
Assume that the universe is in $\bm C$ eigenstate, i.e.
\be
\bm{\tcred{
C|u\rangle = \eta |u\rangle
}}\nonumber
\ee
where $\bm{|\eta|=1}$.\vspace{0.3cm}\\
This means, in particular, that the universe has all zero charges.\\ 
\tcblue{May some
non-zero charge, e.g. ${\bf B}$, be generated dynamically?} \\

\newpage
\noindent
Assume first that C is conserved, i.e.
\be
\tcred{\bm{
\left[ C, {\cal H}\right] = 0
}}\nonumber
\ee 
Time evolution of ${\bf B}$:
\be
\tcblue{\bm{
B(t) = \langle u | e^{-i {\cal H}t} J^B_0 e^{i{\cal H}t} |u\rangle.
}}\nonumber
\ee
Insert $\bm{ I = C^{-1} C}$:
\be
\tcblue{\bm{
B(t) =\langle u| I 
 e^{-i{\cal H}t} I J^B_0 I e^{i{\cal H} t} I
| u \rangle = - B(t) 
}}\nonumber
\ee
taken that ${\bf \tcred{ C J^B_0 C^{-1} = -J_0^B}} $.\vspace{0.3cm}\\
Thus in C-conserving theory $$\bm{B(t)=B_{in}=0}.$$

\newpage
\noindent
The same arguments with ${\bf CP}$ instead of ${\bf C}$ prove
that charge asymmetry cannot be 
generated, if CP is conserved and
\tcred{the universe is an eigenstate of CP:} 
\be
\bm{\tcblue{
CP |u\rangle = \eta |u\rangle
}}\nonumber
\ee

\npni
In globally rotating universe charge asymmetry might be
generated even if CP is conserved.
\tcred{ Global rotation can be 
transformed into baryonic charge}!\\
\tcblue{New long-range interactions, possibly pathological,
are needed??? }\\
Observed predominant galaxy rotations in one direction !?.


\newpage
\noindent
For B-generation in elementary (local) processes no assumption about the universe 
state is necessary:\\ 
\tcblue{if CP is conserved, no asymmetry is generated through particle 
decays or reactions.}\\ 
- discuss below in concrete scenarios.

\npni
\tcblue{CP-breaking in MSM}\\
is absent for two quark families - \\
\tcred{can be rotated away.}\\
\tcblue{Three families are necessary} - an anthropic explanation of number
of flavors? \tcblue{(does not work)}.
\\
If \tcred{masses} of different up or down quarks \tcred{are equal,} 
CP violation can be \tcblue{rotated away} because unit matrix is invariant.\\
If \tcred{mass matrix is diagonal} in the same representation as flavor 
matrix CP-violation can also be \tcblue{rotated away}.

\newpage
\noindent
Thus CP-breaking is proportional to the product of 
\tcred{the mixing angles} and to 
\tcred{the mass differences} of all down and all up quarks:
\be\tcblue{{\bf
A_- \sim sin \theta_{12}\, sin \theta_{23} sin \theta_{31}\, sin\delta}}
\nonumber\\\tcblue{{\bf
(m_t^2-m_u^2)(m_t^2-m_c^2)(m_c^2-m_u^2)}}
\nonumber\\\tcblue{{\bf
(m_b^2-m_s^2)(m_b^2-m_d^2)(m_s^2-m_d^2)/}}\tcred{{\bf M^{12}}}
\nonumber
\ee
At high ${\bf T}$ the characteristic energy where B is not conserved\\ 
${\bf M\geq 100}$ GeV and
\be
\tcred{{\bf A_- \sim 10^{-19}.
}}\nonumber
\ee

\newpage
\noindent
At ${\bf T=0}$ the mass in the denominator is 
\tcblue{the zero-temperature quark mass}
and the CP-odd amplitude is not such vanishingly small.\\
At high T quarks acquire QCD corrections to the \tcred{``mass'' of order T,} 
while in the numerator there are still ``Higgs masses'' or, better to say, 
\tcblue{small Yukawa coupling constants.}\\
Attempts to modify quark dispersion relation at high T,
\tcred{$\bm{ E = E(p,T)}$,} were unsuccessful.

\npni
{More about the usual CP-violation.}\\
\tcblue{CP-odd phases in Dirac mass matrix:}
\be
\tcred{\bm{
{\cal L}_m = m_{ij} \bar q_i q_j \,. 
}}\nonumber
\ee
Diagonal terms ${\bf m_{ii}}$ are \tcred{real} because of Hermicity.
Off-diagonal ${\bf m_{ij}}$ with ${\bf i\neq j}$ can be \tcblue{complex.}
Phase rotation:
\be 
\tcred{\bm{
q_i \rar e^{i\phi_i} q_i\,.
}}\nonumber
\ee
One can change the phase of $\bm{ m_{ij}}$ by 
\be
\tcred{\bm{
m_{ij} \rar e^{i(\phi_i - \phi_j)} m_{ij} \equiv e^{i\phi_{ij}} m_{ij}\,.
}}\nonumber
\ee
\tcblue{Evidently $\bm{ \phi_{12} + \phi_{23} + \phi_{31} =0}$.}\\
Three phases in $\bm{ m_{ij}}$ and 2 conditions, 
\tcred{one arbitrary phase remains.}

\newpage
\noindent
Majorana mass matrix:
\be
\tcred{\bm{
{\cal L}_M = M_{ij} \nu_i C \nu_j \,.
}}\nonumber
\ee
All ${\bf M_{ij}}$ may be \tcblue{complex.}\\
One can kill three phases in ${\bf M_{ii}}$ by 3 phase rotations of 
$\bm{\nu_i}$. No freedom left after that and 
\tcred{three phases of  ${\bf M_{12}, M_{23}}$, \\
and $\bm{M_{31}}$ remain arbitrary.}
\vspace{0.3cm}\\
\tcgreen{A problem:}
How many CP-odd phases are allowed
in the case of both Dirac and Majorana mass matrices?

\npni
{Mechanisms of PBH formation:}\\
\tcblue{PBHs are formed if the density contrast at horizon scale is of
 the order of unity,} \tcred{$\bm{\delta \rho / \rho \sim 1}$.} Hence
PBHs formed at cosmological time $\bm{t_p}$ have masses:
\be \tcred{\bm{
M = t_p m_{Pl}^2,\,\,\,\,\,\, t_p = r_g/2
}}\nonumber
\ee
where $\bm{r_g = 2M/m_{Pl}^2}$ and 
\be \tcblue{\bm{
m_{Pl} = 1.22 \times 10^{19} GeV \approx 2.18\times 10^{-5} g.
}}\nonumber
\ee

\npni
\tcblue{With flat spectrum of perturbations the probability of BH formation is
low, $\bm{\Omega_p \ll 1}$ }. 
{Large density perturbations
at small scales after inflation 
could be created by a massive scalar field with general
renormalizable coupling to the inflaton (AD, J. Silk):}
\be \tcred{\bm{
\lambda (\Phi - \Phi_1)^2 |\chi|^2\,.
}}\nn
\ee
\tcblue{Log-normal mass spectrum of BH.} Discussed below.

\npni
The effective mass behave as \\
\tcred{$\bm{m_{eff}^2 \approx m_0^2 + m_1^4 (t-t_1)^2}$}, 
when $\bm{\Phi}$ passes through ${\bm{\Phi_1}}$. Correspondingly
the dispersion is:
\be\tcblue{\bm{
\langle \chi^2\rangle \sim \left[ m_0^2 + m_1^4 (t-t_1)^2 \right]^{-1}}}
\label{chi2-avrgd-2}
\nonumber
\ee

\npni
\tcblue{Probability for $\bm{\chi}$ to reach a high value}\\ 
is determined by the diffusion equation (Starobinsky):
\be 
\tcred{\bm{
\frac{\partial{\cal P}}{\partial t}=
\frac{H^3}{8\pi^2}\sum_{k=1,2}\frac{\partial^2{\cal P}}{\partial\chi_k^2}+}}
\nonumber \\
\tcred{\bm{\frac{1}{3H}\sum_{k=1,2}\frac{\partial}{\partial\chi_k}
\left[{\cal P}\frac{\partial U} {\partial\chi_k}\right]}}
\label{dP-dt}
\nonumber
\ee
where $\bm{\chi= \chi_1+i\chi_2}$.

\newpage
\noindent
\tcblue{DARK MATTER\\ made out of high B compact objects, 
black holes or dead
(anti)stars. }\vs{0.5cm}\\
\tcred{Normal CDM with new features:} \vs{0.3cm}\\
1. DM ``particles'' have different masses.\\
2. Very heavy ones with \tcblue{${\bm{ M>10^6 M_\odot}}$} should 
exist and may be \tcred{seeds of structure formation.} Lighter stellar
type objects populate galactic halos as usual CDM. 

\newpage
\noindent
\tcblue{No stars are observed in the halo.} It means that 
all high B compact objects are already dead 
or semi-dead stars. Stellar wind
is absent. However, \tcred{annihilation of background protons on  
the surface should exist.} 

\newpage
\noindent
\tcblue{DARK MATTER\\ made out of high B compact objects, 
black holes or dead
(anti)stars. }\vs{0.5cm}\\
\tcred{Normal CDM with new features:} \vs{0.3cm}\\
1. DM ``particles'' have different masses.\\
2. Very heavy ones with \tcblue{${\bm{ M>10^6 M_\odot}}$} should 
exist and may be seeds of structure formation. Lighter stellar
type objects populate galactic halos as usual CDM. 



\newpage
\noindent
\begin{figure}[t]
\begin{center}
\leavevmode
%\vskip 0.2truecm
%\epsfxsize=3.4truein \epsfbox{neutrino_1.eps}
%\epsfxsize=5.7truein \epsfbox{fig3_nu2000.eps}
\epsfxsize=5.7truein \epsfbox{fig3_nu2000.eps}
\end{center}
\end{figure}
\clearpage

\npni
\tcred{Other bounds on PBP=DM see:}\\
I. Reviews by Carr.\\
\tcblue{II. More recent:}\\
1. N. Afshordi, P. McDonald, D. N. Spergel, astro-ph/0302035;\\
2. J. Yoo, J. Chaname, A. Gould, astro-ph/0306437;\\
3. N. Seto, A. Cooray, astro-ph/0702586.\\[2mm]
\tcblue{Results strongly depend upon the mass spectrum.}

\newpage
\noindent
\tcblue{DARK MATTER\\ made out of high B compact objects, 
black holes or dead
(anti)stars. }\vs{0.5cm}\\
\tcred{Normal CDM with new features:} \vs{0.3cm}\\
1. DM ``particles'' have different masses.\\
2. Very heavy ones with \tcblue{${\bm{ M>10^6 M_\odot}}$} should 
exist and may be seeds of structure formation. Lighter stellar
type objects populate galactic halos as usual CDM. 



\newpage
\noindent
\begin{figure}[t]
\begin{center}
\leavevmode
%\vskip 0.2truecm
%\epsfxsize=3.4truein \epsfbox{neutrino_1.eps}
%\epsfxsize=5.7truein \epsfbox{fig3_nu2000.eps}
\epsfxsize=5.7truein \epsfbox{fig3_nu2000.eps}
\end{center}
\end{figure}
\clearpage

\npni
\tcred{Other bounds on PBP=DM see:}\\
I. Reviews by Carr.\\
\tcblue{II. More recent:}\\
1. N. Afshordi, P. McDonald, D. N. Spergel, astro-ph/0302035;\\
2. J. Yoo, J. Chaname, A. Gould, astro-ph/0306437;\\
3. N. Seto, A. Cooray, astro-ph/0702586.\\[2mm]
\tcblue{Results strongly depend upon the mass spectrum.}

\npni
\tcblue{Due to stochastic behavior of $\bm{\theta}$,
this scenario is favorable for creation of cosmologically significant
amount of antimatter.}\\ 
\tcred{However, this and similar scenarios of antimatter 
creation suffer from too
large isocurvature density perturbations at large scales which are
forbidden by CMBR.}



\npni
\tcred{2. Affleck-Dine mechanism,} \tcblue{with a minor 
modification may work pretty well and create plenty of antimatter
quite close to us.}



\npni
\tcblue{Anti-creation scenarios.}\\[3mm]
Discussed above:\\ 
\tcred{spontaneous CP-violation;}\\
\tcblue{mixture of explicit and spontaneous.}\\
Both have serious problems.


\newpage
\noindent
Second equation for the quantum baryonic Dirac field:
\be\tcblue{\bm{
\left(i\partial+m  \right)\psi = -g\eta l+ 
(\partial_\mu\theta) \gamma_\mu \psi
}}\nonumber
\ee
Find solution in one-loop approximation for $\bm{\psi (\theta)}$ 
in external classical
field $\bm{\theta}$ and substitute $\bm{ \bar\psi \psi = F (\theta)}$ into
equation of motion for $\bm{\theta}$.
The solution oscillates with alternating baryonic number. 
Net result:
\be\tcred{\bm{
n_B \sim \eta^2 \Gamma_{\Delta B} (\Delta \theta)^3 .
}}\nonumber
\ee

\npni
\tcblue{The size of empty regions between domain should be smaller than
10 Mpc to avoid noticeable density perturbations,} but this is smaller
than mean free path of photons which brings $\bm{p\bar p}$ into 
contact. 
\tcred{Positive feedback:} annihilation creates excessive pressure 
far from the annihilation zone and push $\bm{p \bar p}$
together. \tcblue{Some loopholes may invalidate this bound.}

\npni
\tcblue{V. Spontaneous baryogenesis.}\\
May operate in thermal equilibrium. \\
Explicit CP-violation is not obligatory.\\
\tcblue{Spontaneous breaking of ${\bf U(1)}$:}
\be\tcred{\bm{
U(\phi) = \lambda (|\phi|^2 - \eta^2)^2 ,
}}\nonumber
\ee
related e.g. to baryonic charge,
leads to massless, Goldstone boson, $\bm{ \theta (x)}$:
\be{\tcred{\bm{
\phi = \eta\, \exp (i\theta)
}}}\nonumber
\ee 
If the potential $\bm{ V(\theta) \neq 0}$ the boson\\ 
would be massive but usually light. E.g.
${\tcblue{\bm{
\delta U(\phi) = m^2 \left(\phi^2 + \phi^{*2}\right)
}}.}$

\newpage
\noindent
In the broken phase the Lagrangian can be written as:
\be\tcblue{\bm{
{\cal L} =\eta^2 (\partial \theta )^2}} + \tcred{\bm{
\partial_\mu \theta j^B_\mu}}\tcblue{\bm{
- V(\theta) + i\bar Q \gamma_\mu \partial_\mu Q + }}\nonumber\\
\tcblue{\bm{
i\bar L \gamma_\mu \partial_\mu L +
(g \eta \bar Q L + h.c.).
}}\nonumber
\ee 
Red term looks like chemical potential, 
$\tcred{\bm{ \dot\theta n_N}}$ but in 
reality is not, because the coupling is derivative 
and \tcblue{${\bm{{\cal L} \neq {\cal H}}}$.}

\newpage
\noindent
If $\bm{ V(\theta) =0}$, i.e. purely Goldstone case, we can 
integrate equation of motion:
\be\tcblue{\bm{
2 \eta^2 \partial^2 \theta = -\partial_\mu j_\mu ^B
}}\nonumber
\ee
and obtain:
\be\tcred{\bm{
\Delta n_B = - \eta^2 \Delta \dot \theta
}}\nonumber
\ee
i.e. non-zero baryon asymmetry in thermal equilibrium and without
explicit CP-violation. The latter is created by initial 
$\tcblue{\bm{ \dot\theta\neq 0}} $.

\newpage
\noindent
In realistic case $\tcblue{\bm{ \dot\theta}}$ is small and 
pseudogoldstone case could be more efficient. %\vspace{0cm}
\\
Equation of motion:
\be\tcblue{\bm{
\eta^2 \ddot \theta +3H\dot \theta}} + \tcred{\bm{ V' (\theta)}} =
\tcblue{\bm{ \partial_\mu j_\mu^B.
}}\nonumber
\ee
with $\bm{ V(\theta) \approx 
m^2 \eta^2\left[-1+ (\theta-\pi)^2 \right]}$\\
and $\bm{ j_\mu^B = \bar\psi \gamma_\mu \psi}$.\\
\tcblue{Initially $\bm{\theta}$ is uniform in $\bm{ [0,2\pi]}$
and after inflation it started to oscillate around minimum.}

\npni
\tcblue{Due to stochastic behavior of $\bm{\theta}$,
this scenario is favorable for creation of cosmologically significant
amount of antimatter.}\\ 
\tcred{However, this and similar scenarios of antimatter 
creation suffer from too
large isocurvature density perturbations at large scales which are
forbidden by CMBR.}


\newpage
\noindent
\tcblue{OBSERVATIONS (reminder):}\\[2mm]
\tcred{Up to now no astronomically significant 
objects consisting antimatter have been observed}. 
A little antiprotons and 
positrons in cosmic rays are most probably of 
\tcred{secondary} origin.\\[2mm]
\tcblue{No unexplained excess of 100 MeV gamma-rays.}\\ 
Antimatter either does not live 
in the universe or it is very far away, \tcred{if
cosmic antimatter is in the same form as matter.}

