Regular two-component bouncing cosmologies and perturbations therein

We present a full investigation of scalar perturbations in a rather generic model for a regular bouncing universe, where the bounce is triggered by an effective perfect fluid with negative energy density. Long before and after the bounce the universe is dominated by a source with positive energy density, which may be a perfect fluid, a scalar field, or any other source with an intrinsic isocurvature perturbation. Within this framework, we present an analytical method to accurately estimate the spectrum of large-scale scalar perturbations until their reentry, long after the bounce. We also propose a simple way to identify non-singular gauge-invariant variables through the bounce and present the results of extensive numerical tests in several possible realizations of the scenario. In no case do we find that the spectrum of the pre-bounce growing mode of the Bardeen potential can be transferred to a post-bounce constant mode.