Holographic Curvature Perturbations in a Cosmology with a Space-Like Singularity

TL;DR

This paper investigates how cosmological perturbations evolve through a space-like singularity in an AdS bulk by using the AdS/CFT correspondence, revealing that the power spectrum's index remains unchanged across the bounce.

Contribution

It demonstrates a method to track perturbations through a singularity by mapping bulk dynamics to boundary gauge fields, maintaining the spectral index.

Findings

The boundary theory simplifies at high curvature, aiding analysis.

Cosmological perturbation spectra are preserved across the singularity.

The approach offers insights into singularity resolution in holographic cosmology.

Abstract

We study the evolution of cosmological perturbations in an anti-de-Sitter (AdS) bulk through a cosmological singularity by mapping the dynamics onto the boundary conformal fields theory by means of the AdS/CFT correspondence. We consider a deformed AdS space-time obtained by considering a time-dependent dilaton which induces a curvature singularity in the bulk at a time which we call $t = 0$, and which asymptotically approaches AdS both for large positive and negative times. The boundary field theory becomes free when the bulk curvature goes to infinity. Hence, the evolution of the fluctuations is under better controle on the boundary than in the bulk. To avoid unbounded particle production across the bounce it is necessary to smooth out the curvature singularity at very high curvatures. We show how the bulk cosmological perturbations can be mapped onto boundary gauge field fluctuations. We evolve the latter and compare the spectrum of fluctuations on the infrared scales relevant for cosmological observations before and after the bounce point. We find that the index of the power spectrum of fluctuations is the same before and after the bounce.