Stability of the Closed Einstein Universe in Energy-Momentum Squared Gravity

Abstract: This paper analyzes the stability of the closed Einstein static universe by using linear homogeneous perturbations in the framework of energy-momentum squared gravity. This newly developed proposal resolves the primordial singularity and yields feasible cosmological results in the early times. For this purpose, we consider the closed Friedmann-Robertson-Walker universe with isotropic matter configuration and adopt small perturbations on the matter parameters and scale factor. Further, we establish equations of motion for static as well as perturbed systems and analyze the stable regions for particular $f(\mathcal{R},\mathbf{T}^{2})$ models corresponding to both conserved and non-conserved energy-momentum tensor. The graphical interpretation demonstrates that stable regions of the Einstein cosmos exist for all values of the model parameters and equation of state variable. We conclude that stable regions in this modified theory are large as compared to other modified theories of gravity.