Quantum fluctuations on a thick de Sitter brane

TL;DR

This paper studies quantum fluctuations on a thick de Sitter brane to determine if its finite thickness naturally regularizes the Kaluza-Klein spectrum, revealing finite amplitudes and divergence behaviors depending on brane dimensions.

Contribution

It demonstrates that brane thickness acts as a natural cutoff for KK modes and analyzes the dependence of mode amplitudes on renormalization scale and brane thickness.

Findings

KK amplitude is finite for finite brane thickness

Thin wall limit recovers standard divergence behaviors

Bound state mode is insensitive to brane thickness at fixed renormalization scale

Abstract

We investigate quantum fluctuations on a de Sitter (dS) brane, which has its own thickness, in order to examine whether or not the finite thickness of the brane can act as a natural cut-off for the Kaluza-Klein (KK) spectrum. We calculate the amplitude of the KK modes and the bound state by using the zeta function method after a dimensional reduction.We show that the KK amplitude is finite for a given brane thickness and in the thin wall limit the standard surface divergent behavior is recovered. The strength of the divergence in the thin wall limit depends on the number of dimensions, e.g., logarithmic on a two dimensional brane and quadratic on a four dimensional brane. We also find that the amplitude of the bound state mode and KK modes depends on the choice of renormalization scale; and for fixed renormalization scales the bound state mode is insensitive to the brane thickness both for two and four-dimensional dS branes.