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.
Highlights
In spite of its many successes, cosmology faces a number of outstanding theoretical and fundamental challenges
In this context the AdS/CFT correspondence could come to use. This correspondence [12] is a proposal for a non-perturbative treatment of string theory and states that the dynamics of a bulk Anti-de Sitter (AdS) space-time that includes gravity is encoded in the boundary of this space-time, where a conformal field theory (CFT) with no gravity lives
The challenge for our work is to explore if the AdS/CFT correspondence can be used to determine the cosmological perturbations in the expanding phase starting with some initial cosmological perturbations in the contracting phase
Summary
We are interested in studying cosmological backgrounds in the context of the AdS/CFT correspondence. Some time-dependent backgrounds in string theory were studied in [25,26,27,28] where the bulk solution can be thought as a time-dependent deformation of AdS5 × S5 with a corresponding N = 4 supersymetric Yang-Mills (SYM) theory with a time dependent gauge coupling constant as a dual theory. We will be interested in considering linear fluctuations of matter and scalar metric degrees of freedom on this surface at some initial time t −tb, and computing the corresponding fluctuations on the same constant z surface in the future of the singularity, once the bulk theory once again becomes weakly coupled, i.e. at t = tb. Let us turn to the CFT description of our solution In this time-dependent background, the dual boundary theory is a N = 4 SYM theory with a source. This coupling goes to zero as t → 0 and the CFT becomes free
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