  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.
