Constraining f(R) theories with cosmography

TL;DR

The paper introduces a novel cosmography-based method to constrain f(R) gravity theories by comparing series expansions of observables, providing tighter bounds on model parameters than previous approaches.

Contribution

It presents a new approach using cosmography to set constraints on extended gravity theories, applicable to f(R) models with improved precision.

Findings

Limits on f(R) parameters are more stringent than previous constraints.

The method successfully constrains previously unconstrained parameters.

Application to specific models demonstrates the method's effectiveness.

Abstract

A method to set constraints on the parameters of extended theories of gravitation is presented. It is based on the comparison of two series expansions of any observable that depends on H(z). The first expansion is of the cosmographical type, while the second uses the dependence of H with z furnished by a given type of extended theory. When applied to f(R) theories together with the redshift drift, the method yields limits on the parameters of two examples (the theory of Hu and Sawicki (2007), and the exponential gravity introduced by Linder (2009)) that are compatible with or more stringent than the existing ones, as well as a limit for a previously unconstrained parameter.