A Note on the Generalized Friedmann Equations for a Thick Brane

TL;DR

This paper investigates how the thickness of a brane in a five-dimensional spacetime affects cosmological equations, revealing that brane thickness, and consequently fundamental constants like G and Lambda, can vary over time.

Contribution

It explicitly demonstrates the necessity of time-varying brane thickness for consistency with energy conservation in a thick brane model.

Findings

Brane thickness generally evolves over time.

Newton's constant G can be time-dependent.

Effective cosmological constant Lambda_4 can vary with time.

Abstract

Within our thick brane approach previously used to obtain the cosmological evolution equations on a thick brane embedded in a five-dimensional Schwarzschild Anti-de Sitter spacetime it is explicitly shown that the consistency of these equations with the energy conservation equation requires that, in general, the thickness of the brane evolves in time. This varying brane thickness entails the possibility that both Newton's gravitational constant $G$ and the effective cosmological constant $\Lambda_4$ are time dependent.