Consequences of a Stabilizing Field's Self-Interactions for RS Cosmology

TL;DR

This paper investigates how self-interactions of the stabilizing field in Randall-Sundrum models influence the phase transition, bubble nucleation rate, and gravitational wave signals, revealing that cubic self-interactions can enhance transition rates and modify GW signatures.

Contribution

It introduces a cubic term in the Goldberger-Wise scalar potential, showing how self-interactions affect the radion potential and phase transition dynamics in RS cosmology.

Findings

Cubic self-interactions deepen the radion potential and increase radion mass.

The phase transition rate is enhanced, reducing supercooling.

Gravitational wave signals are increased in frequency but decreased in strength, remaining detectable.

Abstract

It has been argued that the Randall-Sundrum (RS) phase transition rate is suppressed when the holographic theory corresponds to a large $N$ Yang-Mills and when the stabilizing field has a small mass. Here we argue that self-interactions can alleviate the latter suppression. We consider a cubic term in the bulk potential for the Goldberger-Wise (GW) scalar that is responsible for stabilizing the RS geometry. Adding a cubic term suffices to separate the two roles of the GW stabilization: generating a large hierarchy and triggering confinement. We study the resulting radion potential and the dynamics of the early universe phase transition. For a negative coefficient of the cubic term, the effect of the cubic becomes important in the infra-red, and the resulting radion potential is deeper, thereby increasing the radion mass while maintaining a large hierarchy. Staying within the radion effective field theory, we calculate the rate of bubble nucleation from the hot phase to the confined RS phase, both in thin and thick wall limits. The cubic term enhances the rate and allows relaxing the condition on the maximum number of colors $N_\text{max}$ of the dual theory for which the phase transition can be completed. Importantly, this reduces the amount of supercooling that the false vacuum undergoes, increases the peak frequency of the gravitational waves (GW) produced from bubble collisions, and reduces the strength of the GW signal. The reduced GW signal is however still within the reach of proposed space-based GW detectors.