Gravitational waves and cosmological braneworlds: a characteristic evolution scheme

TL;DR

This paper develops a numerical scheme to study bulk gravitational waves in braneworld cosmology, showing that the late-time gravitational wave spectrum remains flat and robust against initial data uncertainties, challenging naive 4D predictions.

Contribution

A new characteristic evolution scheme for 1+1D wave equations with moving boundaries, applicable to braneworld scenarios, and analysis of initial condition effects on gravitational wave spectra.

Findings

Late-time waveform is insensitive to initial data surface if set far in the past.

The stochastic gravitational wave spectrum is predominantly flat.

Flat spectrum is robust against initial data uncertainties at high inflation energy scales.

Abstract

Motivated by the problem of the evolution of bulk gravitational waves in Randall-Sundrum cosmology, we develop a characteristic numerical scheme to solve 1+1 dimensional wave equations in the presence of a moving timelike boundary. The scheme exhibits quadratic convergence, is capable of handling arbitrary brane trajectories, and is easily extendible to non-AdS bulk geometries. We use our method to contrast two different prescriptions for the bulk fluctuation initial conditions found in the literature; namely, those of Hiramatsu et al. (hep-th/0410247) and Ichiki and Nakamura (astro-ph/0406606). We find that if the initial data surface is set far enough in the past, the late time waveform on the brane is insensitive to the choice between the two possibilities; and we present numeric and analytic evidence that this phenomenon generalizes to more generic initial data. Observationally, the main consequence of this work is to re-affirm previous claims that the stochastic gravitational wave spectrum is predominantly flat, in contradiction with naive predictions from the effective 4-dimensional theory. Furthermore, this flat spectrum result is predicted to be robust against uncertainties in (or modifications of) the bulk initial data, provided that the energy scale of brane inflation is high enough.