First law of thermodynamics and entropy of FLRW universe in modified gravity

TL;DR

This paper explores the thermodynamics and entropy of the apparent horizon in FLRW universes within various modified gravity theories, deriving entropy formulas and reconstructing gravitational Lagrangians consistent with the first law.

Contribution

It provides a method to derive entropy formulas based on apparent horizon radius in second-order modified gravity theories and reconstructs compatible gravitational Lagrangians.

Findings

Entropy can be expressed solely in terms of the apparent horizon radius.

Modified gravity theories allow for a generalized entropy formula.

Reconstruction of gravitational Lagrangians consistent with thermodynamic laws.

Abstract

We investigate the first law of thermodynamics and entropy associated to the apparent horizon of (non-flat) FLRW space-time in different theories of modified gravity and in the presence of a perfect fluid of matter. We pose our attention on those theories which lead to second order differential field equations on FLRW background. In this way, we observe that one may obtain a formula for entropy in terms of the radius of the apparent horizon only. Thus, when considering a modification to the area law of General Relativity, it is possible to reconstruct the gravitational lagrangian consistent with the corresponding first law.