A general thermodynamical description of the event horizon in the FRW universe

TL;DR

This paper derives the Friedmann equation from thermodynamic principles on the event horizon in FRW universes, incorporating quantum corrections and modified gravity theories, and explores the laws of thermodynamics in these contexts.

Contribution

It provides a unified thermodynamic framework for the evolution of FRW universes, including quantum effects and alternative gravity models, extending previous work on horizon thermodynamics.

Findings

Friedmann equations derived from the first law of thermodynamics on the event horizon.

Quantum corrections and $f(R)$ gravity effects incorporated into universe evolution.

Validation of the generalized second law of thermodynamics in different gravity theories.

Abstract

The Friedmann equation in the Friedmann-Robertson-Walker(FRW) universe with any spatial curvature is derived from the first law of thermodynamics on the event horizon. The key idea is to redefine a Hawking temperature on the event horizon. Furthermore, we obtain the evolution equations of the universe including the quantum correction and explore the evolution of the universe in the $f(R)$ gravity. In addition, we also investigate the generalized second law of thermodynamics in Einstein gravity and the $f(R)$ gravity. This perspective also implies that the first law of thermodynamics on the event horizon have a general description in respect of the evolution of the FRW universe.