AdS / CFT correspondence in cosmology

The attempt to understand if AdS/CFT correspondence may be realized as the one between some AdS-like cosmological space and CFT living on the boundary is made. In order to obtain such cosmology we exchange the time and radial coordinates in d5 Schwarzschild-anti de Sitter (S-AdS) BH (with corresponding signature change). The test on proportionality of free energies from such d5 cosmological space (after AdS/CFT identification of parameters) and from N = 4 SU(N) super Yang-Mills quantum theory is successfully passed. email: [email protected] 2 email: [email protected], [email protected] 1 AdS/CFT correspondence [1] in its simplest version may be understood as duality between 5d gravity and quantum CFT living on its boundary (for a review, see [2]). One remarkable feature of this duality is that calculations in classical gravity on d5 AdS background may provide the answers for dual quantum CFT. Very beatiful example of this sort is given by calculation of free energy for d5 S-AdS BH [3, 4] which turns out to be almost equal to free energy of maximally SUSY Yang-Mills theory in the leading approximation on large N . The natural question is: can we extend above test (or, more generally whole AdS/CFT correspondence) to cosmology and how it could be realized on practice? In the present note we try to answer this question working with specific AdS-like cosmological model obtained by exchange of radial and time coordinates in S-AdS BH. Calculating analog of free energy for such cosmological model one can show that it gives (almost) free energyof maximally SUSY Yang-Mills theory but with another mismatch factor than in S-AdS BH case. We start with the following action of 5-dimensional gravity with negative cosmological constant Λ = − 12 L < 0: S = 1 κ ∫