Causal Structure and Gravitational Waves in Brane World Cosmology

TL;DR

This paper investigates the causal structure of flat brane universes in RSII models, clarifies boundary conditions for gravitational waves, and proposes a numerical method to solve related equations, enhancing understanding of gravitational wave behavior in higher-dimensional cosmologies.

Contribution

It introduces a new analysis of the causal structure and boundary conditions for gravitational waves in brane world models, along with a numerical procedure applicable to scalar perturbations.

Findings

Identification of the 'seam singularity' in gravitational wave equations.

Development of a numerical method for gravitational wave boundary conditions.

Examples demonstrating the numerical procedure's effectiveness.

Abstract

The causal structure of the flat brane universe of RSII type is re-investigated to clarify the boundary conditions for stochastic gravitational waves. In terms of the Gaussian normal coordinate of the brane, a singularity of the equation for gravitational waves appears in the bulk. We show that this singularity corresponds to the ``seam singularity'' which is a singular subspace on the brane universe. Based upon the causal structure, we discuss the boundary conditions for gravitational waves in the bulk. Introducing a null coordinate, we propose a numerical procedure to solve gravitational waves with appropriate boundary conditions and show some examples of our numerical results. This procedure could be also applied in scalar type perturbations. The problem in the choice of the initial condition for gravitational waves is briefly discussed.