Cosmological perturbations on a bouncing brane

Abstract

The cosmological perturbations on a bouncing brane are studied. The brane is movinginside a Klebanov–Strassler throat where the infrared region of the geometry is smoothlycut off. For an observer confined to the world volume of the brane, this results in anon-singular bouncing mirage cosmology. We have calculated the scalar perturbationscorresponding to the normal displacements of the brane. This is performed in the probebrane 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 acontracting to an expanding phase. We find that the spectral index of the dominantmode of the metric fluctuation is unchanged, unlike what is obtained by gluingcontracting to expanding Einstein universes with the help of the usual matchingconditions. Assuming that the fluctuations start off in a vacuum state on sub-Hubblescales during the contracting phase, it is shown that the resulting spectral indexns on super-Hubble scales in the expanding phase has a large blue tilt. When the brane is movingslowly inside the throat and its kinetic energy is negligible compared to its rest mass, one findsns = 3. For a fast-rolling brane with a large kinetic energy, the spectral index isns = 2.3. This may put severe constraints on models of mirage cosmology.