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

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.