Kinematic reconstructions of extended theories of gravity at small and intermediate redshifts

Abstract

In the last few decades, extensions of General Relativity have reached always more attention especially in view of possible breakdowns of the standard ΛCDM paradigm at intermediate and high redshift regimes. If General Relativity would not be the ultimate theory of gravity, modifying Einstein's gravity in the homogeneous and isotropic universe may likely represent a viable path toward the description of current universe acceleration. We here focus our attention on two classes of extended theories, i.e. the f (R) and f (R, G)-gravity. We parameterize the so-obtained Hubble function by means of effective barotropic fluids, by calibrating the shapes of our curves through some of the most suitable dark energy parameterizations, XCDM, CPL, WP. Afterwards, by virtue of the correspondence between the Ricci scalar and the Gauss-Bonnet topological invariant with the redshift z, we rewrite f (R, G) in terms of corresponding f (z) auxiliary functions. This scheme enables one to get numerical shapes for f (R, G) and f (R) models, through a coarse-grained inverse scattering procedure. Although our procedure agrees with the simplest extensions of general relativity, it leaves open the possibility that the most suitable forms of f (R) and f (R, G) are rational Padé polynomials of first orders. These approximations seem to be compatible with numerical reconstructions within intermediate redshift domains and match fairly well small redshift tests. *

Kinematic constraints beyond z ≃ 0 using calibrated GRB correlations

“…There is an apparent (9 ± 2.5)% tension between H 0 measured by the Planck Collaboration VI (2020) and Riess et al (2018), respectively. Other significant evidence in favor of not yet understood new physics comes from the potential driving inflationary times, which is written in excellent approximation in terms of a Starobinsky R + αR 2 correction of Einstein's gravity (Planck Collaboration VI 2020;Calzá et al 2020). The question is thus: are there new physics beyond the concordance paradigm?…”

A Confront between Amati and Combo Correlations at Intermediate and Early Redshifts

“…Thus, the need of model-independent techiques is essential to overcome the above issues [35,[40][41][42][43][44][45][46][47][48][49]49,50]. However, the model is plagued by the convergence problem [51].…”

Generalized Gibbons-Werner method for stationary spacetimes

“…Researchers have utilized the JMRF metric, as well as its specific forms, to investigate the gravitational deflection of particles [48-54, 58, 63, 75-89], the Kepler orbit [90], the motion of charged particles [91], and Hawking radiation [92,93]. A comprehensive discussion on the JMRF metric can be found in [94].…”