# Bouncing scenario in $f(R,T)$ gravity

## TL;DR

This paper models a matter bounce in $f(R,T)$ gravity, showing that the universe avoids initial singularity, but the bounce is highly unstable, with perturbations decaying rapidly afterward, ensuring late-time stability.

## Contribution

It introduces a matter bounce model in $f(R,T)$ gravity with a non-vanishing scale factor, analyzing stability and energy condition violations near the bounce.

## Key findings

- Initial conditions are finite, avoiding singularity.
- Energy conditions are violated near the bounce.
- Model is highly unstable at the bounce but stable at late times.

## Abstract

The present manuscript presents modeling of matter bounce in the framework of $f(R,T)$ gravity where $f(R,T) = R + 2 \lambda T$. We start by defining a parametrization of scale factor which is non-vanishing. The geometrical parameters such as the Hubble parameter and deceleration parameter are derived, from which expressions of pressure, density and Equation of State (EoS) parameter and a qualitative understanding of the initial conditions of the universe at the bounce are ascertained. We found that the initial conditions of the universe are finite owing to the non-vanishing nature of the scale factor thus eliminates the initial singularity problem. Furthermore, we show the violation of energy conditions near the bouncing region and analyzed the stability of our model with respect to linear homogeneous perturbations in Friedmann-Lema\^tre-Robertson-Walker (FLRW) spacetime. We found that our model and hence matter bounce scenarios in general are highly unstable at the bounce in the framework of $f(R,T)$ gravity but the perturbations decay out rapidly away from the bounce safeguarding its stability at late times.