First Law of Thermodynamics and Friedmann Equations of Friedmann-Robertson-Walker Universe

TL;DR

This paper derives the Friedmann equations of the universe from thermodynamic principles applied to the apparent horizon, extending to theories with modified entropy-area relations like Gauss-Bonnet and Lovelock gravity.

Contribution

It presents a unified thermodynamic derivation of Friedmann equations across different gravity theories, including those with non-area proportional entropy.

Findings

Friedmann equations derived from thermodynamics for various gravity theories.

Extension of thermodynamic derivation to Gauss-Bonnet and Lovelock gravity.

Discussion of physical implications of modified entropy relations.

Abstract

Applying the first law of thermodynamics to the apparent horizon of a Friedmann-Robertson-Walker universe and assuming the geometric entropy given by a quarter of the apparent horizon area, we derive the Friedmann equations describing the dynamics of the universe with any spatial curvature. Using entropy formulae for the static spherically symmetric black hole horizons in Gauss-Bonnet gravity and in more general Lovelock gravity, where the entropy is not proportional to the horizon area, we are also able to obtain the Friedmann equations in each gravity theory. We also discuss some physical implications of our results.