Extended gravity cosmography

Abstract

Cosmography can be considered as a sort of a model-independent approach to tackle the dark energy/modified gravity problem. In this review, the success and the shortcomings of the [Formula: see text]CDM 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 [Formula: see text] and [Formula: see text] theories of gravity where dynamics is represented by curvature or torsion field, respectively. The features of [Formula: see text] models are explored in metric and Palatini formalisms. We discuss the connection between [Formula: see text] gravity and scalar–tensor theories highlighting the role of conformal transformations in the Einstein and Jordan frames. Cosmological dynamics of [Formula: see text] 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 [Formula: see text] 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 model-independent 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 [Formula: see text] and [Formula: see text] functions and to frame the late-time expansion history of the universe with no a priori assumptions on its equation-of-state. A comparison between the [Formula: see text]CDM cosmological model with [Formula: see text] and [Formula: see text] models is reported.