Constructions of entropy and modified Friedmann equations in gravity theories

Abstract

The FRW universe is considered a thermodynamical system. We assume that the universe filled in a perfect fluid. So, we obtain apparent horizon radius, surface gravity, and temperature. Using the unified first law as well as the first law of thermodynamics and Friedmann equations, we obtain the entropy-area relation on the apparent horizon in Einstein’s gravity. In Horava–Lifshitz gravity, scalar–tensor gravity, f(R) gravity and f(T) gravity theories, using corresponding Friedmann equations, we obtain the corresponding entropies in integration forms. Next, for a power law, future singularity, and de Sitter expansions, we obtain the general entropy function F(A) in terms of horizon area A on different IR cutoffs like Hubble, apparent, particle, event, (m, n)-type event, conformal age, and Ricci horizons. Moreover, by considering general entropy, we determine the modified Friedmann equations for Horava–Lifshitz gravity, scalar–tensor gravity, f(R) gravity and f(T) gravity theories.