Brane-world and loop cosmology from a gravity-matter coupling perspective

TL;DR

This paper demonstrates how brane-world and loop quantum cosmology expansion histories can be modeled using a modified gravity framework involving non-minimal matter coupling, providing analytical solutions without second-order constraints.

Contribution

It introduces a reconstruction method for deriving $f(R)$ and $g(R)$ functions in modified gravity that replicate specific cosmological histories, especially in the Palatini formalism.

Findings

Reconstruction algorithm yields analytical solutions for cosmological models.

In simplest cases, $f(R)$ is quadratic and $g(R)$ is linear in $R$.

No second-order constraint needed in Palatini formalism.

Abstract

We show that the effective brane-world and the loop quantum cosmology background expansion histories can be reproduced from a modified gravity perspective in terms of an $f(R)$ gravity action plus a $g(R)$ term non-minimally coupled with the matter Lagrangian. The reconstruction algorithm that we provide depends on a free function of the matter density that must be specified in each case and allows to obtain analytical solutions always. In the simplest cases, the function $f(R)$ is quadratic in the Ricci scalar, $R$, whereas $g(R)$ is linear. Our approach is compared with recent results in the literature. We show that working in the Palatini formalism there is no need to impose any constraint that keeps the equations second-order, which is a key requirement for the successful implementation of the reconstruction algorithm.