Comprehensive Analysis of a Non-Singular Bounce in $f(R,T)$ Gravitation

The present paper is devoted to the study of bouncing cosmology in $f(R,T)$ modified gravity where we presume $f(R,T) = R + 2 \lambda T$, with $R$ the Ricci scalar, $T$ the trace of energy momentum tensor and $\lambda$ the model parameter. We present here a novel parametrization of Hubble parameter which is apt in representing a successful bouncing scenario undergoing no singularity. We proceed to present a complete analysis of the proposed bouncing model by studying the evolution of primordial curvature perturbations, energy conditions and stability against linear homogeneous perturbations in flat space-time. We also delineate bouncing cosmology for the proposed model by employing Quintom matter. The present article further communicate for the first time that violation of energy-momentum materialize for both the contracting and expanding universes except for the bouncing epoch with energy flow directed away and into the matter fields for the contracting and expanding universe respectively. We further present a thorough investigation about the feasibility of the proposed bouncing scenario against first and generalized second law of thermodynamics. We found that the proposed bouncing scenario obeys the laws of thermodynamics for the constrained parameter space of $\lambda$. The manuscript conclude after investigating the viability of the proposed bouncing model in non minimal $f(R,T)$ gravity where $f(R,T) = R + \chi R T$.