New Horizons in Bouncing Cosmology: Viable Solutions in <i>f</i> (ℝ, <i>T</i> ² ) Gravity

In this paper, we investigate bouncing cosmological solutions to examine cosmic evolution in energy-momentum squared gravity. For this purpose, we explore the behavior of a flat Friedmann-Robertson-Walker spacetime with a perfect matter configuration. A specific form of the f(ℝ,T 2 ) model is chosen to examine how this modified framework affects cosmic dynamics. By deriving and analyzing the corresponding modified field equations, we examine symmetric bounce, oscillatory bounce and matter bounce scenarios. Stability of these models is also investigated through linear perturbation analysis. Our findings reveal that the null energy condition is violated at the bounce point, a necessary condition for achieving a successful bounce. Moreover, the behavior of the equation of state parameter indicates the accelerated cosmic expansion. These results demonstrate that energy-momentum squared gravity offers a compelling alternative to the standard cosmological models.