Can Inflating Braneworlds be Stabilized?

TL;DR

This paper analyzes the stability of scalar perturbations in inflating braneworld models with extra dimensions, revealing a tachyonic instability for de Sitter branes and proposing a new mechanism for primordial fluctuation generation.

Contribution

It provides a self-consistent calculation of scalar fluctuations in warped five-dimensional braneworlds with de Sitter slices, identifying conditions for stability and a novel fluctuation mechanism.

Findings

Radion mass squared is negative for inflating branes, indicating instability.

Stabilized de Sitter branes are prone to tachyonic instability.

A new scale-free primordial fluctuation mechanism occurs when radion mass is below Hubble parameter.

Abstract

We investigate scalar perturbations from inflation in braneworld cosmologies with extra dimensions. For this we calculate scalar metric fluctuations around five dimensional warped geometry with four dimensional de Sitter slices. The background metric is determined self-consistently by the (arbitrary) bulk scalar field potential, supplemented by the boundary conditions at both orbifold branes. Assuming that the inflating branes are stabilized (by the brane scalar field potentials), we estimate the lowest eigenvalue of the scalar fluctuations - the radion mass. In the limit of flat branes, we reproduce well known estimates of the positive radion mass for stabilized branes. Surprisingly, however, we found that for de Sitter (inflating) branes the square of the radion mass is typically negative, which leads to a strong tachyonic instability. Thus, parameters of stabilized inflating braneworlds must be constrained to avoid this tachyonic instability. Instability of "stabilized" de Sitter branes is confirmed by the BraneCode numerical calculations in the accompanying paper hep-th/0309001. If the model's parameters are such that the radion mass is smaller than the Hubble parameter, we encounter a new mechanism of generation of primordial scalar fluctuations, which have a scale free spectrum and acceptable amplitude.