Thermodynamics and Perturbative Analysis of Some Newly Developed F(R,Lm,T)$\mathcal {F}(R,L_m, T)$ Theories Under the Scenario of Conserved Energy‐momentum Tensor

Abstract

AbstractThe present work is devoted to explore some interesting cosmological features of a newly proposed theory of gravity namely theory, where R and T represent the Ricci scalar and trace of energy momentum‐tensor, respectively. First, a non‐equilibrium thermodynamical description is considered on the apparent horizon of the Friedmann's cosmos. The Friedmann equations are demonstrated to be equivalent to the first law of thermodynamics, i.e., , where refers to entropy production term. The constraint for validity of generalized second law of thermodynamics is also formulated and checked it for some simple well‐known forms of generic function . Next, the energy bounds for this framework and constraint the free variables by finding the validity regions for NEC and WEC are developed. Furthermore, some interesting cosmological solutions namely power law, ΛCDM, and de Sitter models in this theory are reconstructed. The reconstructed solutions are then examined by checking the validity of GSLT and energy bounds. Lastly, the stability of all reconstructed solutions by introducing suitable perturbations in the field equations is analyzed. It is concluded that obtained solutions are stable and cosmologically viable.