Evolution of gravitational waves in the high-energy regime of brane-world cosmology

TL;DR

This paper investigates how gravitational waves evolve in a high-energy brane-world cosmology, revealing that Kaluza-Klein mode excitations suppress GW amplitudes, affecting the stochastic GW background.

Contribution

It provides a numerical analysis of GW evolution in a five-dimensional brane-world, highlighting the impact of KK-modes and early universe transitions on GW amplitudes.

Findings

GW amplitude on the brane is insensitive to transition timing if early enough.

KK-modes cause suppression of GW amplitude, counteracting non-standard expansion effects.

High-energy effects significantly influence the stochastic GW background.

Abstract

We discuss the cosmological evolution of gravitational waves (GWs) after inflation in a brane-world cosmology embedded in five-dimensional anti-de Sitter (AdS_5) bulk spacetime. In a brane-world scenario, the evolution of GWs is affected by the non-standard cosmological expansion and the excitation of the Kaluza-Klein modes (KK-modes), which are significant in the high-energy regime of the universe. We numerically solve the wave equation of GWs in the Poincare coordinates of the AdS_5 spacetime. Using a plausible initial condition from inflation, we find that, while the behavior of GWs in the bulk is sensitive to the transition time from inflation to the radiation dominated epoch, the amplitude of GWs on the brane is insensitive to this time if the transition occurs early enough before horizon re-entry. As a result, the amplitude of GWs is suppressed by the excitation of KK-modes which escape from the brane into the bulk, and the effect may compensate the enhancement of the GWs by the non-standard cosmological expansion. Based on this, the influence of the high-energy effects on the stochastic background of GWs is discussed.