A Nonsingular Logarithmic Bouncing Cosmology in $f(R,T)$ Gravity with Thermodynamic Viability

Abstract

We present a nonsingular bouncing cosmological model in the framework of modified $f(R,T)$ gravity within a spatially flat Friedmann--Robertson--Walker universe. A logarithmic time-dependent scale factor is assumed to realize a smooth transition from a contracting phase to an expanding phase without encountering an initial singularity. Based on this assumption, the dynamical evolution of the Hubble parameter, deceleration parameter, energy density, and pressure is obtained for various choices of the model and the matter--geometry coupling parameter to confirm the occurrence of a successful bounce. The effective equation of state parameter is examined to characterize the cosmic fluid during different evolutionary phases. The violation of energy conditions, necessary for the realization of the bouncing behavior, is also discussed. The stability of the model is investigated using the squared speed of sound and is found to remain positive within the allowed parameter space, indicating classical stability. Furthermore, constraints on the matter--geometry coupling parameter are obtained by demanding positive energy density, negative pressure, and a viable cosmological evolution. The obtained cosmological constraint on the coupling parameter is also shown to be compatible with the currently available compact-object constraints. The thermodynamic behavior of the model is examined by testing the generalized second law of thermodynamics. The total entropy production rate remains negative during the contracting phase and changes its sign to positive during the expanding phase. However, it becomes singular at the bouncing point, reflecting the breakdown of the standard thermodynamic description during the transition phase.