2023•arXiv (Cornell University)Open access

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

Lorenzo Sebastiani

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.

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Key concepts: Friedmann–Lemaître–Robertson–Walker metric, Apparent horizon, Second law of thermodynamics, Entropy (arrow of time), Physics, General relativity, Gravitation, H-theorem