Perturbations on a moving D3-brane and mirage cosmology

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 $\varphi (\tau ,\vec{x})$. We derive an equation of motion for $\varphi$, 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 $\varphi$ is proportional to the gauge invariant Bardeen potentials on the brane.

26 pages, 5 figures, to appear in Phys.Rev.D, comments and minor corrections added

References in corpus (1)

• Gauge invariant cosmological perturbation theory for braneworlds

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