2009/07/31 by Axel Kleinschmidt, Michael Koehn, Hermann Nicolai
Physics and Astronomy · #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #Particle physics theoretical and experimental studies #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.80.061701
published as Phys.Rev.D80:061701,2009 · 4 pages. v2: Added ref. Version to be published in PRD
arxiv created 2009/09/18 · openalex publication_date 2009/09/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
D=11 supergravity near a spacelike 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 wave functions involving automorphic (Maass wave) forms under the modular group W+(E10)\ensuremath≅PSL2(\mathttO) 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.