Cosmological equations and Thermodynamics on Apparent Horizon in Thick Braneworld

TL;DR

This paper derives generalized cosmological equations for a thick braneworld model with curvature corrections and shows their equivalence to thermodynamic laws on the apparent horizon.

Contribution

It introduces a unified framework for cosmological evolution and thermodynamics in thick braneworlds with curvature corrections, extending previous thin-brane models.

Findings

Derivation of generalized Friedmann equations with curvature corrections.

Identification of two effective 4D reductions of the equations.

Reformulation of the equations as the first law of thermodynamics on the apparent horizon.

Abstract

We derive the generalized Friedmann equation governing the cosmological evolution inside the thick brane model in the presence of two curvature correction terms: a four-dimensional scalar curvature from induced gravity on the brane, and a five-dimensional Gauss-Bonnet curvature term. We find two effective four-dimensional reductions of the Friedmann equation in some limits and demonstrate that they can be rewritten as the first law of thermodynamics on the apparent horizon of thick braneworld.