Stability Analysis of Some Reconstructed Cosmological Models in $f(\mathcal{G},T)$ Gravity

TL;DR

This paper reconstructs and analyzes the stability of various cosmological models in $f( ext{G},T)$ gravity, focusing on de Sitter and power-law solutions, and assesses their stability against linear perturbations.

Contribution

It introduces a reconstruction method for cosmological models in $f( ext{G},T)$ gravity and performs stability analysis of key solutions, which is novel in this modified gravity context.

Findings

De Sitter and power-law solutions are reconstructed in $f( ext{G},T)$ gravity.

Stability conditions for these solutions are derived and analyzed.

Certain models exhibit stable behavior under linear perturbations.

Abstract

The aim of this paper is to reconstruct and analyze the stability of some cosmological models against linear perturbations in $f(\mathcal{G},T)$ gravity ($\mathcal{G}$ and $T$ represent the Gauss-Bonnet invariant and trace of the energy-momentum tensor, respectively). We formulate the field equations for both general as well as particular cases in the context of isotropic and homogeneous universe model. We reproduce the cosmic evolution corresponding to de Sitter universe, power-law solutions and phantom/non-phantom eras in this theory using reconstruction technique. Finally, we study stability analysis of de Sitter as well as power-law solutions through linear perturbations.