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

The 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.

Wormhole solutions under the effect of dark matter in f(R, L m ) gravity

“…Also, in geometry-matter couplings [16], it is shown that the matter content of the wormhole is remarkably able to obey the energy conditions. There are a number of modified gravity theories that have been proposed in the literature [17][18][19][20][21][22][23][24][25][26][27][28][29] to get around the undetectable exotic matter.…”

“…Substituting the value of c 1 in equation (21) we get, graphical representation is shown in the figure1. Now, the incorporation of equation(23) into equations (17)-(19) for the NEC regarding radial and tangential pressures at the throat r = r 0 can be uniquely expressed as By performing another integration on equation(20) with α = 3 to determine the shape function b (r), using the throat condition b(r 0 ) = r 0 , we arrive at the following result…”