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

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.

13 pages, 2 figures

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• The Cosmological OTOC: Formulating new cosmological micro-canonical correlation functions for random chaotic fluctuations in Out-of-Equilibrium Quantum Statistical Field Theory
• Fluctuations through a Vibrating Bounce
• Big Bounce Genesis and Possible Experimental Tests -- A Brief Review
• Solution of the cosmological constant problem within holographic cosmology
• Quantum Hořava-Lifshitz cosmology in the de Broglie-Bohm interpretation
• Holographic cosmology from "dimensional reduction" of $\mathcal{N}=4$ SYM vs. $Ad{S}_5\times S^5$
• Following the density perturbations through a bounce with AdS/CFT Correspondence