Dynamics of a singularity-free universe in f(R,T2) Gravity

This study investigates bouncing cosmological solutions to understand cosmic evolution in the background of $f(R,T^2)$ theory, where $R$ denotes the Ricci scalar and $T^2=T^{\xi \eta }{T}_{\xi \eta }$ is the self-contraction of the stress energy tensor. For this purpose, we analyze a flat Friedmann–Robertson–Walker spacetime with perfect matter distribution and assume a specific functional form of $f(R,T^2)$ theory to explore the effects of modified gravity on cosmic dynamics. Further, we evaluate super bounce and exponential bounce models to investigate the non-singular universe in this framework. The positive behavior of energy density and the negative behavior of pressure, as well as null energy condition ensure the existence of a viable cosmological bounce solutions. The equation of state parameter indicates the phantom region corresponding to the super bounce model and the quintessence era for exponential bounce model, indicating that the universe experiences cosmic acceleration. The stability of the obtained solutions is analyzed through linear perturbation, demonstrating the model’s robustness against small fluctuations and confirming its validity as a framework for understanding cosmic evolution. Our findings suggest that this modified gravitational theory provides an alternative framework to standard cosmology, offering insights into gravitational interactions and the early cosmic evolution.