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 ΛCDM 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. We discuss the connection between f (R) gravity and scalar-tensor 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 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 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 f (R) and f (T ) functions and to frame the late-time expansion history of the universe with no a priori assumptions on April 3, 2019 0:31 WSPC/INSTRUCTION FILE Review 2 S. Capozziello, R. D'Agostino, O. Luongo its equation of state. A comparison between the ΛCDM cosmological model with f (R) and f (T ) models is reported.

Connecting early and late epochs by f(z)CDM cosmography

“…s 0 = −0.1 ± 0.6 in 1σ, and also the constraints on the cosmological and cosmographic parameters do not change with respect to the case where s 0 was fixed to zero (green line). Noteworthy, the s 0 parameter constrained is in fully agreement with the previous results [21], showing a worse constraint than the other cosmographic parameters.…”

“…A possibility, widely studied in the literature, is to provide higher order corrections related to the geometry of the universe (coming as remnants of quantum fluctuations in early universe [49,50,51]). In this context, several Extended Theories of Gravity 2 have been tested, addressing phenomenology ranging from the primordial inflationary expansion to the current accelerated behavior [10,11,21]. Among these, it is particularly promising the Starobinsky model [53,54] that, according to the recent CMBR data, is one of the best candidate to fit inflationary behavior with the possibility to address also the recent dark energy behavior [55,56].…”

Cosmographic analysis of redshift drift

“…and delay the explicit use of the Einstein equations for as long as possible. Cosmographic ideas have become increasingly popular over the last two decades [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37].…”

High-redshift cosmography: auxiliary variables versus Padé polynomials

“…A feasible consequence of this scheme is the stability of these new expansions over a large redshift interval. Examples of this approach are the Padé and Chebyshev rational polynomials (Wei, Yan & Zhou 2014;Gruber & Luongo 2014;Capozziello, D'Agostino & Luongo 2018a,b;Capozziello, Ruchika & Sen 2019;Capozziello, D'Agostino & Luongo 2019;Benetti & Capozziello 2019).…”