# Following the density perturbations through a bounce with AdS/CFT Correspondence

## TL;DR

This paper uses AdS/CFT correspondence to analyze the bounce universe model, demonstrating that the primordial density perturbation spectrum remains stable and scale-invariant through the bounce, despite strong coupling near the bounce point.

## Contribution

It introduces a holographic approach to study the bounce dynamics, showing the preservation of the primordial spectrum's scale invariance across the bounce.

## Key findings

- Primordial density spectrum remains stable through the bounce.
- Holographic duality allows controlled evolution of perturbations.
- Scale invariance of the spectrum is preserved during the bounce.

## Abstract

A bounce universe model, known as the coupled-scalar-tachyon bounce (CSTB) universe, has been shown to solve the Horizon, Flatness and Homogeneity problems as well as the Big Bang Singularity problem. Furthermore a scale invariant spectrum of primordial density perturbations generated from the phase of pre-bounce contraction is shown to be stable against time evolution. In this work we study the detailed dynamics of the bounce and its imprints on the scale invariance of the spectrum. The dynamics of the gravitational interactions near the bounce point may be strongly coupled as the spatial curvature becomes big. There is no a prior reason to expect the spectral index of the primordial perturbations of matter density can be preserved. By encoding the bounce dynamics holographically onto the dynamics of dual Yang-Mills system while the latter is weakly coupled, via the AdS/CFT correspondence, we can safely evolve the spectrum of the cosmic perturbations with full control. In this way we can compare the post-bounce spectrum with the pre-bounce one: in the CSTB model we explicitly show that the spectrum of primordial density perturbations generated in the contraction phase preserves its stability as well as scale invariance throughout the bounce process.