Perturbations on a moving D3-brane and mirage cosmology

TL;DR

This paper investigates how perturbations evolve on a moving D3-brane in an AdS-Schwarzschild background, revealing conditions for stability and growth of fluctuations, and connecting brane perturbations to cosmological scalar potentials.

Contribution

It derives the equation of motion for brane perturbations and analyzes their behavior in different regimes, linking brane dynamics to cosmological perturbations.

Findings

Superhorizon modes grow as a^4 on expanding BPS branes with E=0

All modes grow during brane contraction

Perturbed brane embedding relates to gauge-invariant Bardeen potentials

Abstract

We study the evolution of perturbations on a moving probe D3-brane coupled to a 4-form field in an AdS$_5$-Schwarzschild bulk. The unperturbed dynamics are parametrised by a conserved energy $E$ and lead to Friedmann-Robertson-Walker `mirage' cosmology on the brane with scale factor $a(\tau)$. The fluctuations about the unperturbed worldsheet are then described by a scalar field $\phi(\tau,\vec{x})$. We derive an equation of motion for $\phi$, and find that in certain regimes of $a$ the effective mass squared is negative. On an expanding BPS brane with E=0 superhorizon modes grow as $a^4$ whilst subhorizon modes are stable. When the brane contracts, all modes grow. We also briefly discuss the case when $E>0$, BPS anti-branes as well as non-BPS branes. Finally, the perturbed brane embedding gives rise to scalar perturbations in the FRW universe. We show that $\phi$ is proportional to the gauge invariant Bardeen potentials on the brane.