Generating Cosmological Perturbations in Ekpyrotic, Rapid-Bounce Scenarios

Abstract

We present a mechanism which yields a non-singular bounce that transitions a slowly-contracting universe to the expanding, radiation-dominated one of the Big Bang model. The same mechanism enhances the vacuum spectra of both curvature and gravitational wave perturbations produced during slow-contraction and converts them into nearly scale-invariant spectra. We extend the work done by [1] to include in this result not only the case of an instantaneous, delta-function bounce but also gradual, square-well bounces. We also generalize to a hydrodynamical stressenergy associated with the bounce without any reference to S-Branes or other microphysical descriptions. Using a time-dependent equation of state for this matter, the tilts are calculated for the curvature and tensor perturbations in the square-well case, and in contrast to [1] we do not nd that these tilts the same. The amplitude of the gravitational wave spectrum is found to be exponentially higher than that of the curvature spectrum and is therefore inconsistent with observations; more work must be done to bring this into observational tolerance.