Supersymmetric quantum cosmological billiards

Details Supersymmetric quantum cosmological billiards Supersymmetric quantum cosmological billiards

2009-07-17

arxiv.org/abs/0907.3048v2

Phys.Rev.D80:061701,2009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

4 pages. v2: Added ref. Version to be published in PRD

Scientific paper

10.1103/PhysRevD.80.061701

D=11 Supergravity near a space-like singularity admits a cosmological billiard description based on the hyperbolic Kac-Moody group E10. The quantization of this system via the supersymmetry constraint is shown to lead to wavefunctions involving automorphic (Maass wave) forms under the modular group W^+(E10)=PSL(2,O) with Dirichlet boundary conditions on the billiard domain. A general inequality for the Laplace eigenvalues of these automorphic forms implies that the wave function of the universe is generically complex and always tends to zero when approaching the initial singularity. We discuss possible implications of this result for the question of singularity resolution in quantum cosmology and comment on the differences with other approaches.

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