Bouncing cosmological solutions from f(R,T) gravity

TL;DR

This paper explores classical bouncing cosmological solutions within a specific $f(R,T)$ gravity framework, demonstrating stable, nonsingular bouncing scenarios with potential violations of energy conditions, and linking effective fluid descriptions to generalized equations of state.

Contribution

It introduces a reformulation using an effective fluid in $f(R,T)$ gravity to find stable, nonsingular bouncing solutions and analyzes their properties and stability.

Findings

Bouncing solutions exhibit de-Sitter phases before and after the bounce.

Most models show stability against scalar perturbations with slight transient fluctuations.

Some energy conditions are violated near the bounce, but solutions remain nonsingular and stable.

Abstract

In this work we study classical bouncing solutions in the context of $f({\sf R},{\sf T})={\sf R}+h({\sf T})$ gravity in a flat {\sf FLRW} background using a perfect fluid as the only matter content. Our investigation is based on introducing an effective fluid through defining effective energy density and pressure; we call this reformulation as the "effective picture". These definitions have been already introduced to study the energy conditions in $f({\sf R},{\sf T})$ gravity. We examine various models to which different effective equations of state, corresponding to different $h({\sf T})$ functions, can be attributed. It is also discussed that one can link between an assumed $f({\sf R},{\sf T})$ model in the effective picture and the theories with generalized equation of state ({\sf EoS}). We obtain cosmological scenarios exhibiting a nonsingular bounce before and after which the Universe lives within a de-Sitter phase. We then proceed to find general solutions for matter bounce and investigate their properties. We show that the properties of bouncing solution in the effective picture of $f({\sf R},{\sf T})$ gravity are as follows: for a specific form of the $f({\sf R,T})$ function, these solutions are without any future singularities. Moreover, stability analysis of the nonsingular solutions through matter density perturbations revealed that except two of the models, the parameters of scalar-type perturbations for the other ones have a slight transient fluctuation around the bounce point and damp to zero or a finite value at late times. Hence these bouncing solutions are stable against scalar-type perturbations. It is possible that all energy conditions be respected by the real perfect fluid, however, the null and the strong energy conditions can be violated by the effective fluid near the bounce event.