Fluctuations in a cosmology with a spacelike singularity and their gauge theory dual description

Abstract

We consider a time-dependent deformation of anti-de-Sitter (AdS) space-time which contains a spacelike "singularity" -a space-like region of high curvature. Making use of the AdS/CFT correspondence we can map the bulk dynamics onto the boundary. The boundary theory has a time dependent coupling constant which becomes small at times when the bulk space-time is highly curved. We investigate the propagation of small fluctuations of a test scalar field from early times before the bulk singularity to late times after the singularity. Under the assumption that the AdS/CFT correspondence extends to deformed AdS space-times, we can map the bulk evolution of the scalar field onto the evolution of the boundary gauge field. The time evolution of linearized fluctuations is well defined in the boundary theory as long as the coupling remains finite, so that we can extend the boundary perturbations to late times after the singularity. Assuming that the spacetime in the future of the singularity has a weakly coupled region near the boundary, we reconstruct the bulk fluctuations after the singularity crossing making use of generic properties of boundary-to-bulk propagators. Finally, we extract the spectrum of the fluctuations at late times given some initial spectrum. We find that the spectral index is unchanged, but the amplitude increases due to the squeezing of the fluctuations during the course of the evolution. This investigation can teach us important lessons on how the spectrum of cosmological perturbations passes through a bounce which is singular from the bulk point of view but which is resolved using an ultraviolet complete theory of quantum gravity.

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".…”