  The cosmological perturbations on a bouncing brane are studied. The brane is
moving inside a Klebanov-Strassler throat where the infra-red region of the
geometry is smoothly cut off. For an observer confined to the world-volume of
the brane, this results in a non-singular bouncing mirage cosmology. We have
calculated the scalar perturbations corresponding to the normal displacements
of the brane. This is performed in the probe brane limit where the
gravitational back-reaction of the brane on the bulk throat is absent. Our
model provides a framework for studying the transfer of fluctuations from a
contracting to an expanding phase. We find that the spectral index of the
dominant mode of the metric fluctuation is un-changed, unlike what is obtained
by gluing contracting to expanding Einstein universes with the help of the
usual matching conditions. Assuming that the fluctuations start off in a vacuum
state on sub-Hubble scales during the contracting phase, it is shown that the
resulting spectral index n_s on super-Hubble scales in the expanding phase has
a large blue tilt. When the brane is moving slowly inside the throat and its
kinetic energy is negligible compared to its rest mass, one finds n_s=3. For a
fast-rolling brane with a large kinetic energy, the spectral index is n_s =
2.3. This may put severe constraints on models of mirage cosmology.
