Extended gravity cosmography
Abstract
Cosmography can be considered as a sort of a modelindependent approach to tackle the dark energy/modified gravity problem. In this review, the success and the shortcomings of the ΛCDM model, based on General Relativity (GR) and standard model of particles, are discussed in view of the most recent observational constraints. The motivations for considering extensions and modifications of GR 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. We discuss the connection between f(R) gravity and scalartensor theories highlighting the role of conformal transformations in the Einstein and Jordan frames. Cosmological dynamics of f(R) models is investigated through the corresponding viability criteria. Afterwards, the equivalent formulation of GR (Teleparallel Equivalent General Relativity (TEGR)) 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 Padé and Chebyshev polynomials, is proposed to overcome limits of standard cosmography based on Taylor expansion. The approach provides accurate modelindependent approximations of the Hubble flow. Numerical analyses, based on Monte Carlo Markov Chain integration of cosmic data, 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 latetime expansion history of the universe with no a priori assumptions on its equationofstate. A comparison between the ΛCDM cosmological model with f(R) and f(T) models is reported.
 Publication:

International Journal of Modern Physics D
 Pub Date:
 2019
 DOI:
 10.1142/S0218271819300167
 arXiv:
 arXiv:1904.01427
 Bibcode:
 2019IJMPD..2830016C
 Keywords:

 Extended gravity;
 cosmography;
 dark energy;
 cosmological observations;
 04.50.‑h;
 04.20.Cv;
 98.80.Jk;
 Fundamental problems and general formalism;
 Mathematical and relativistic aspects of cosmology;
 General Relativity and Quantum Cosmology;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 High Energy Physics  Theory
 EPrint:
 82 pages, 35 figures. Accepted for publication in IJMPD