  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.
