Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-12-27
Physics
High Energy Physics
High Energy Physics - Theory
91 pages, 24 figures; minor reorganization of introduction, clarifying comments throughout
Scientific paper
The AdS/CFT correspondence allows us to map a dynamical cosmology to a dual quantum field theory living on the boundary of spacetime. Specifically, we study a five-dimensional model cosmology in type IIB supergravity, where the dual theory is an unstable deformation of $\N=4$ supersymmetric SU(N) gauge theory on $\Rbar\times S^3$. A one-loop computation shows that the coupling governing the instability is asymptotically free, so quantum corrections cannot turn the potential around. The big crunch singularity in the bulk occurs when a boundary scalar field runs to infinity, in finite time. Consistent quantum evolution requires that we impose boundary conditions at infinite scalar field, {\it i.e.} a self-adjoint extension of the system. We find that quantum spreading of the homogeneous mode of the boundary scalar leads to a natural UV cutoff in particle production as the wavefunction for the homogeneous mode bounces back from infinity. Translating back to the bulk theory, we find that a quantum transition from a 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 naturally small. We comment on qualitative differences with holographic descriptions of large black holes, on four-dimensional generalizations and on implications for cosmological perturbations.
Craps Ben
Hertog Thomas
Turok Neil
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