---
abstract: 'We study the evolution of cosmological perturbations in a non-singular bouncing cosmology with a bounce phase which has superimposed oscillations of the scale factor. We identify length scales for which the final spectrum of fluctuations obtains imprints of the non-trivial bounce dynamics. These imprints in the spectrum are manifested in the form of damped oscillation features at scales smaller than a characteristic value and an increased reddening of the spectrum at all the scales as the number of small bounces increases.'
author:
- Robert Brandenberger
- Qiuyue Liang
- 'Rudnei O. Ramos'
- Siyi Zhou
title: Fluctuations through a Vibrating Bounce
---

Introduction
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Some bouncing cosmologies provide an alternative to cosmological inflation as a way to obtain primordial cosmological fluctuations (see, e.g., Ref. [@BP] for a recent review). Specifically, in a model which contains a matter-dominated phase of contraction, initial vacuum fluctuations in the far past which exit the Hubble radius during the matter-dominated contracting phase evolve into a scale-invariant spectrum of cosmological perturbations [@FB; @Wands]. For example, in the case of an Ekpyrotic contracting universe [@Ekp] entropy fields can source scale-invariant curvature fluctuations [@newEkp]. In all bouncing cosmologies, new physics is required in order to obtain 