Evolution of gravitational waves in Randall-Sundrum cosmology

TL;DR

This paper studies how gravitational waves evolve in a five-dimensional brane-world cosmology, focusing on mode generation during inflation and radiation, and introduces techniques to analyze mode interactions at finite energies.

Contribution

It presents a detailed analysis of gravitational wave mode evolution in Randall-Sundrum cosmology, including the generation of zero and massive modes and perturbative methods for mode-mixing.

Findings

Zero mode generated during inflation

Massive modes remain in vacuum during inflation

Mode decoupling in low-energy limit

Abstract

We investigate the evolution of gravitational wave perturbations about a brane cosmology embedded in a five-dimensional anti-de Sitter bulk. During slow-roll inflation in a Randall-Sundrum brane-world, the zero mode of the 5-dimensional graviton is generated, while the massive modes remain in their vacuum state. When the zero mode re-enters the Hubble radius during radiation domination, massive modes are generated. We show that modes decouple in the low-energy/near-brane limit and develop perturbative techniques to calculate the mode-mixing at finite energy.