Speaker
Description
Cosmography can be considered as a sort of a
model-independent approach to tackle the dark energy/modified gravity
problem. In this talk, the success and the shortcomings of the
$\Lambda$CDM model, based on General Relativity and standard model of
particles, are discussed in view of the most recent observational
constraints. The motivations for considering extensions and modifications
of General Relativity are taken into account, with particular attention to
$f(R)$ and $f(T)$ theories of gravity where dynamics is represented by
curvature or torsion field respectively. The features of $f(R)$ models
are explored in metric and Palatini formalisms.
Cosmological dynamics of $f(R)$ models is investigated through the
corresponding viability criteria. Afterwards, the equivalent formulation
of General Relativity (Teleparallel Equivalent General Relativity) in
terms of torsion and its extension to $f(T)$ gravity is considered.
Finally, the cosmographic method is adopted to break the degeneracy among
dark energy models. A novel approach, built upon rational Pad\'e and
Chebyshev polynomials, is proposed to overcome limits of standard
cosmography based on Taylor expansion. The approach provides accurate
model-independent approximations of the Hubble flow. Numerical analyses
are presented to bound coefficients of the cosmographic series. These
techniques are thus applied to reconstruct $f(R)$ and $f(T)$ functions
and to frame the late-time expansion history of the universe with no
\emph{a priori} assumptions on its equation of state. A comparison
between the $\Lambda$CDM cosmological model with $f(R)$ and $f(T)$ models
is reported.
