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

We discuss the evolution of gravitational waves (GWs) after inflation in a brane-world cosmology embedded in five-dimensional anti-de Sitter (AdS5) 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 (KK) modes, which are significant in the high-energy regime of the universe. We numerically solve the wave equation of GWs in the Poincaré coordinates of the AdS5 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 reentry. As a result, the amplitude of GWs is suppressed by the excitation of KK-modes 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 GW backgrounds is discussed.