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.

Holographic cosmology from “dimensional reduction” of N = 4 SYM vs. AdS5× S5

“…Another holographic approach was developed in [6][7][8], and we will present it in a way that can fit into the holographic cosmology paradigm from the previous section.…”

“…But this holographic cosmology paradigm is more general than the specific class of phenomenological models: it includes standard inflationary cosmology, where the gravitational side is weakly coupled, as well as intermediate coupling field theory models, that can be treated non-perturbatively on the lattice. 1 Another approach to holographic cosmology was considered in [6][7][8], where one starts with a "top down" construction (a well-defined gravity dual pair, derived as the decoupling limit of some system of branes), specifically a modified version of the original N = 4 SYM vs. string theory in AdS 5 ×S 5 , where an FLRW cosmology with a(t) replaces the Minkowski metric, and a nontrivial dilaton is introduced. On the field theory side, one has a timedependent coupling now.…”

“…On the field theory side, one has a timedependent coupling now. The model has been used in [7,8] to show how perturbations entering a Big Crunch exit after the Big Bang, one issue that has been very contentious in ekpyrotic and cyclic cosmologies. It was shown that the spectral index of perturbations exits unchanged, but there was no simple mechanism in [7,8] of calculating the power spectrum of fluctuations for CMBR.…”

“…A natural question to ask then is: can one modify the top down construction of [6][7][8], 1 Lattice work on this is ongoing.…”

Solution of the cosmological constant problem within holographic cosmology

“…. A concrete proposal for such a holographic correspondence between cosmology and a field theory was only developed in [2] (there were other attempted constructions, like for instance the top-down one in [3,4], based on the earlier [5], but they are not so well developed, or general). In the model, a holographic computation, based on the methods of [6][7][8], relates the correlators of fluctuations of h ij observed in the * Electronic address: horatiu.nastase@unesp.br sky, δh ij δh kl , with boundary correlators T ij T kl , in a super-renormalizable 2+1 dimensional field theory with "generalized conformal symmetry".…”