First law of thermodynamics and Friedmann-like equations in braneworld cosmology

TL;DR

This paper derives Friedmann-like equations in braneworld cosmology using thermodynamic principles, linking horizon thermodynamics with gravity models like Randall-Sundrum II and Dvali-Gabadadze-Porrati.

Contribution

It introduces a method to derive cosmological equations from thermodynamics in braneworld models, emphasizing the role of boundary conditions and horizon entropy.

Findings

Thermodynamics on the brane encodes gravity behavior.

Derived equations connect horizon thermodynamics with braneworld gravity.

Israel's boundary condition is crucial in the derivation.

Abstract

We derive the Friedmann-like equations in braneworld cosmology by imposing the first law of thermodynamics and Bekenstein's area-entropy formula on the apparent horizon of a Friedmann-Roberston-Walker universe in both Randall-Sundrum II gravity and Dvali-Gabadadze-Porrati gravity models. Israel's boundary condition plays an important role in our calculations in both cases, besides the first law of thermodynamics and Bekenstein's area-entropy formula. The results indicate that thermodynamics on the brane world knows the behaviors of gravity.