Cosmological Perturbations on a Bouncing Brane

TL;DR

This paper investigates scalar cosmological perturbations on a bouncing brane within a warped throat geometry, revealing that the spectral index remains unchanged during the bounce but can exhibit a large blue tilt, constraining mirage cosmology models.

Contribution

It introduces a framework for analyzing perturbation transfer in bouncing brane cosmology, showing the spectral index remains unchanged across the bounce and depends on brane dynamics.

Findings

Spectral index remains unchanged during the bounce.

Large blue tilt in the spectral index for different brane velocities.

Constraints on mirage cosmology models based on spectral tilt.

Abstract

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.