Speaker
Dr
Surajit Chattopadhyay
(PCMT, Kolkata)
Description
Pilgrim dark energy (PDE) model is studied in this paper and Hubble horizon has been used as
an IR cutoff. The basic assumption of this model is that phantom acceleration prevents the formation of the BH. The said PDE is considered in a modified gravity $f(T,
T_G)$, which has been constructed by Kofinas and Saridakis (2014) on
the basis of $T$ (old quadratic torsion scalar) and $T_G$ (new
quartic torsion scalar $T_G$ that is the teleparallel equivalent of
the Gauss-Bonnet term). We have compiled our work in two phases:
Firstly, we have assumed different scale factors such as $a(t)=a_0
t^m$, $H=H_0+\frac{H_1}{t}$, $a(t)=exp(At^m)$ and
$a(t)=a_0+\alpha(t-t_0)^{2n}$. We have reconstructed $f$ and
subsequently $w_{DE}$ in this scenario. Secondly, we have assumed
analytic function such $f=b_0+b_1~t+b_2~t^2+b_3~t^3$ and
reconstructed Hubble parameter and $w_{DE}$ without any choice of
scale factor.
Throughout the study, we have considered $s=-2$ and $s=2$,
separately. We have observed that $s=-2$, as described in PDE (Wei,
2012), seems more realistic choice for $s$ than $s=2$ and this
outcome of the present reconstruction work is consistent with Wei
(2012). Moreover, it has been observed that the reconstructed
$w_{DE}$, irrespective of choices of scale factor or a choice of
$f$, exhibit a more aggressive phantom-like behavior for $s=-2$ than
$s=2$. This result also matches the study of Wei (2012). Hence, it
is finally concluded that PDE, when considered in $f(T,T_G)$ gravity
is capable of attaining the phantom phase of the universe.
Summary
We work on the reconstruction scenario of pilgrim
dark energy" (PDE) in $f(T, T_G)$. In PDE
model it is assumed that a repulsive force that is accelerating the Universe is phantom type
with $(w_{DE}<-1)$ and it so strong that prevents formation of the black hole. We construct the
$f(T, T_G)$ models and correspondingly evaluate equation of state
parameter for various choices of scale factor. Also, we assume
polynomial form of $f(T, T_G)$ in terms of cosmic time and
reconstruct $H$ and $w_{DE}$ in this manner. Through discussion, it
is concluded that PDE shows aggressive phantom-like behavior for
$s=-2$ in $f(T, T_G)$ gravity.
