Generalized Friedmann Equations for a Finite Thick Brane

TL;DR

This paper derives generalized Friedmann equations for a finite thick brane in a 5D Schwarzschild Anti-de Sitter spacetime, revealing new terms affecting cosmological evolution and conditions for late-time acceleration.

Contribution

It introduces a novel formulation of Friedmann equations for thick branes, including linear density terms and effects on the effective cosmological constant.

Findings

Standard cosmology recovered at late times

Effective 4D cosmological constant depends on brane thickness

Conditions for late-time acceleration identified

Abstract

We present the generalized Friedmann equations describing the cosmological evolution of a finite thick brane immeresed in a five-dimensional Schwarzschild Anti-de Sitter spacetime. A linear term in the density in addition to a quatratic one arises in the Friedmann equation, leading to the standard cosmological evolution at late times without introducing an ad hoc tension term for the brane. The effective four-dimensional cosmological constant is then uplifted similar to the KKLT effect and vanishes for a brane thickness equal to the AdS curvature size, up to the third order of the thickness. The four-dimensional gravitational constant is then equal to the five-dimensional one divided by the AdS curvature radius, similar to that derived by dimensional compactification. An accelerating brane cosmology may emerge at late times provided there is either a negative transverse pressure component in the brane energy-momentum tensor or the effective brane cosmological constant is positive.