Wave Propagation and Scattering for the RS2 Brane Cosmology Model

TL;DR

This paper analyzes gravitational wave behavior in the RS2 brane cosmology model, revealing a combination of localized massless waves and dispersive massive waves, with detailed scattering and decay properties.

Contribution

It provides a comprehensive analysis of wave propagation, decay estimates, and scattering theory for gravitational waves in the RS2 brane cosmology model, including explicit computations of the scattering matrix and resonances.

Findings

Solutions include localized massless waves and dispersive massive waves.

Established decay estimates and Strichartz inequalities for the wave solutions.

Developed a complete scattering theory with asymptotic completeness and resonance analysis.

Abstract

We study the wave equation for the gravitational waves in the Randal-Sundrum brane cosmology model. We solve the global Cauchy problem and we establish that the solutions are the sum of a slowly decaying massless wave localized near the brane, and a superposition of massive dispersive waves. We compute the kernel of the truncated resolvent. We prove some $L^1-L^{\infty}$, $L^2-L^{\infty}$ decay estimates and global $L^p$ Strichartz type inequalities. We develop the complete scattering theory : existence and asymptotic completeness of the wave operators, computation of the scattering matrix, determination of the resonances on the logarithmic Riemann surface.