Causal Structure and Gravitational Waves in Brane World Cosmology

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.

9 pages, 6 figures, accepted for publication in PRD; this version includes the referee's suggestions and expanded discussion on our numerical scheme

References in corpus (2)

• Evolution of gravitational waves from inflationary brane-world : numerical study of high-energy effects
• Evolution of gravitational waves in Randall-Sundrum cosmology

Cited by in corpus (15)

• Brane-World Gravity
• Brane-world gravity
• Braneworld resonances
• Gravitational waves and extra dimensions: a short review
• The spectrum of gravitational waves in Randall-Sundrum braneworld cosmology
• Late time behavior of cosmological perturbations in a single brane model
• Evolution of gravitational waves in the high-energy regime of brane-world cosmology
• Dynamical Casimir effect for gravitons in bouncing braneworlds
• Quantum-mechanical generation of gravitational waves in braneworld
• High-energy effects on the spectrum of inflationary gravitational wave background in braneworld cosmology
• Gravitational waves and cosmological braneworlds: a characteristic evolution scheme
• Coupled bulk and brane fields about a de Sitter brane
• Initial Kaluza-Klein fluctuations and inflationary gravitational waves in braneworld cosmology
• Scalar perturbations in braneworld cosmology
• Numerical study of curvature perturbations in a brane-world inflation at high-energies