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Physical Review D 86 (2012) 043513
Quantum Resolution of Cosmological Singularities using AdS/CFT
B. Craps1, T. Hertog1, 2, 3, N. Turok

The AdS/CFT correspondence is used to describe five-dimensional cosmology with a big crunch singularity in terms of N=4 supersymmetric SU(N) gauge theory on R times S^3 deformed by an unstable potential. In this boundary field theory, a one-loop computation shows that the coupling governing the instability is asymptotically free, so that quantum corrections cannot turn the potential around. The big crunch singularity in the bulk corresponds in the boundary theory to a scalar field rolling to infinity in finite time. We generalize the method of self-adjoint extensions to define consistent unitary quantum evolution in the boundary theory. The quantum mechanical spread of the wave function for the homogeneous mode on the sphere suppresses the creation of high energy particles as the scalar field rolls down the potential and bounces back. This leads to the prediction that a quantum transition from the big crunch to a big bang is the most probable outcome of cosmological evolution, for a specific parameter range. Intriguingly, the instability and approximate scale-invariance of the boundary theory lead to the generation of an approximately scale-invariant spectrum of stress-energy perturbations on the boundary, whose amplitude is suppressed by the asymptotically free coupling. We comment on qualitative differences with holographic descriptions of large black holes, on four-dimensional generalizations and on implications for cosmological perturbations.
1 :  International Solvay Institutes
2 :  APC - UMR 7164 - AstroParticule et Cosmologie
3 :  Institute for Theoretical Physics
Physique/Physique des Hautes Energies - Théorie
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