New integrable models and analytical solutions in $f(R)$~cosmology with an ideal gas

TL;DR

This paper identifies new integrable $f(R)$ gravity models with ideal gas matter content, providing analytical and closed-form solutions for these cosmological theories.

Contribution

It introduces three new families of integrable $f(R)$ models and derives their analytical solutions using invariant transformation methods.

Findings

Three new integrable $f(R)$ models are proposed.

Analytical solutions are explicitly derived for these models.

Closed-form solutions are obtained, enhancing understanding of $f(R)$ cosmology.

Abstract

In the context of $f\left( R\right) $-gravity with a spatially flat FLRW metric containing an ideal fluid, we use the method of invariant transformations to specify families of models which are integrable. We find three families of $f(R)$ theories for which new analytical solutions are given and closed-form solutions are provided.