Cosmological perturbations in bouncing cosmologies and the case of the Pre-Big Bang scenario

The Pre-Big Bang cosmology inspired generations of cosmologists in attempts to cure the initial Big Bang singularity using a fundamental length scale as proposed by String Theory. The existence of a phase of collapse/inflation with increasing curvature followed by a cosmic bounce has been proposed as an alternative to standard inflation in the solution of the horizon and curvature problems. However the generation of a nearly scale-invariant spectrum of perturbations is not an automatic prediction of such scenarios. In this paper I review some general statements about the evolution of perturbations in bouncing cosmologies and some historically significant attempts to reconcile the predicted spectra with the observations. Bouncing cosmologies and in particular the Pre-Big Bang scenario stand as viable, although more complicated, alternatives to inflation that may still help solve current theoretical and observational tensions.