Generalized entropies and the expansion law of the universe

TL;DR

This paper employs the first law of thermodynamics to derive the universe's expansion law and dynamic equations in various gravity theories, offering a unified thermodynamic approach to cosmology.

Contribution

It introduces a thermodynamic method to derive expansion laws and Friedmann equations for different gravity models, including deformed Horava-Lifshitz, f(R), and scalar-tensor gravities.

Findings

Derived the expansion law for a Kodama observer.

Obtained the dynamic equation of FRW universe in deformed Horava-Lifshitz gravity.

Presented a new thermodynamic approach to derive Friedmann equations for f(R) and scalar-tensor gravities.

Abstract

We suggest that using the first law of thermodynamics is a convenient method to obtain a correct form of the expansion law of the universe \cite{T. Padmanabhan1}. We will, then, use this idea to obtain the expansion law for a Kodama observer. By using the expansion law for a Kodama observer, we can obtain the dynamic equation of the FRW universe for deformed Horava-Lifshitz gravity. The use of the first law of thermodynamics also leads to a new approach for obtaining the Friedmann equations for f(R) and scalar tensor gravities.