The spectrum of gravitational waves in Randall-Sundrum braneworld cosmology

TL;DR

This paper investigates the generation and evolution of gravitational waves in Randall-Sundrum braneworld cosmology, demonstrating that modifications to the standard spectrum are minimal due to cancellation of dominant effects, with some dark radiation produced.

Contribution

The study provides a detailed numerical analysis of gravitational wave spectra in braneworld cosmology, confirming the cancellation of dominant effects and quantifying dark radiation production.

Findings

Initial vacuum fluctuations in Kaluza-Klein modes are subdominant.

The spectral tilt remains consistent with the standard four-dimensional result.

A tiny amount of dark radiation is generated from escaping Kaluza-Klein gravitons.

Abstract

We study the generation and evolution of gravitational waves (tensor perturbations) in the context of Randall-Sundrum braneworld cosmology. We assume that the initial and final stages of the background cosmological model are given by de Sitter and Minkowski phases, respectively, and they are connected smoothly by a radiation-dominated phase. This setup allows us to discuss the quantum-mechanical generation of the perturbations and to see the final amplitude of the well-defined zero mode. Using the Wronskian formulation, we numerically compute the power spectrum of gravitational waves, and find that the effect of initial vacuum fluctuations in the Kaluza-Klein modes is subdominant, contributing not more than 10% of the total power spectrum. Thus it is confirmed that the damping due to the Kaluza-Klein mode generation and the enhancement due to the modification of the background Friedmann equation are the two dominant effects, but they cancel each other, leading to the same spectral tilt as the standard four-dimensional result. Kaluza-Klein gravitons that escape from the brane contribute to the energy density of the dark radiation at late times. We show that a tiny amount of the dark radiation is generated due to this process.