Updated constraints on $f(\mathcal{R})$ gravity from cosmography

TL;DR

This paper uses cosmography to constrain $f( ext{R})$ gravity models, deriving bounds on their derivatives from observational data, and proposes a viable $f( ext{R})$ candidate consistent with late-time cosmic acceleration.

Contribution

It introduces a model-independent cosmographic approach to constrain $f( ext{R})$ gravity and identifies a candidate function compatible with observational data.

Findings

$f( ext{R})$ models are consistent with cosmological data

Derived bounds on $f(z)$ and its derivatives up to fourth order

Proposed a viable $f( ext{R})$ function reproducing late-time acceleration

Abstract

We address the issue of constraining the class of $f(\mathcal{R})$ able to reproduce the observed cosmological acceleration, by using the so called cosmography of the universe. We consider a model independent procedure to build up a $f(z)$-series in terms of the measurable cosmographic coefficients; we therefore derive cosmological late time bounds on $f(z)$ and its derivatives up to the fourth order, by fitting the luminosity distance directly in terms of such coefficients. We perform a Monte Carlo analysis, by using three different statistical sets of cosmographic coefficients, in which the only assumptions are the validity of the cosmological principle and that the class of $f(\mathcal{R})$ reduces to $\Lambda$CDM when $z\ll1$. We use the updated union 2.1 for supernovae Ia, the constrain on the $H_0$ value imposed by the measurements of the Hubble space telescope and the Hubble dataset, with measures of $H$ at different $z$. We find a statistical good agreement of the $f(\mathcal{R})$ class under exam, with the cosmological data; we thus propose a candidate of $f(\mathcal{R})$, which is able to pass our cosmological test, reproducing the late time acceleration in agreement with observations.