Perturbations on a moving D3-brane and mirage cosmology

We study the evolution of perturbations on a moving probe D3-brane coupled to a four-form field in an AdS(5)-Schwarzschild bulk. The unperturbed dynamics are parametrized by a conserved energy E and lead to a Friedmann-Robertson-Walker (FRW) "mirage" cosmology on the brane with a scale factor a(tau). The fluctuations about the unperturbed worldsheet are then described by a scalar field phi(tau,(x) over right arrow). 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 Bogomol'nyi-Prasad-Sommerfield (BPS) brane with E=0 superhorizon modes grow as a(4) while subhorizon modes are stable. When the brane contracts, all modes grow. We also briefly discuss the case when E>0, BPS antibranes 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.