# Stability Analysis of Einstein Universe in $f(\mathcal{G},T)$ Gravity

## TL;DR

This study examines the stability of the Einstein universe within $f( ext{G},T)$ gravity, identifying conditions under which the universe remains stable against linear homogeneous perturbations through analytical and graphical methods.

## Contribution

It provides a detailed stability analysis of the Einstein universe in $f( ext{G},T)$ gravity, considering both conserved and non-conserved energy-momentum tensors, which is a novel extension.

## Key findings

- Stable regions depend on parameter choices.
- Graphical analysis confirms stability conditions.
- Stability varies with the equation of state parameter.

## Abstract

This paper explores stability of the Einstein universe against linear homogeneous perturbations in the background of $f(\mathcal{G},T)$ gravity. We construct static as well as perturbed field equations and investigate stability regions for the specific forms of generic function $f(\mathcal{G},T)$ corresponding to conserved as well as non-conserved energy-momentum tensor. We use the equation of state parameter to parameterize the stability regions. The graphical analysis shows that the suitable choice of parameters lead to stable regions of the Einstein universe.