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  Cosmological Quantum Billiards

Nicolai, H., & Kleinschmidt, A. (2011). Cosmological Quantum Billiards. In J. Murugan, & A. Weltman (Eds.), Foundations of Space and Time: Reflections on Quantum Gravity. Cambridge: Cambridge University Press.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0012-641E-F Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0012-6421-5
Genre: Book Chapter

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0912.0854v2.pdf (Any fulltext), 296KB
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 Creators:
Nicolai, Hermann1, Author              
Kleinschmidt, Axel1, Author              
Affiliations:
1Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, escidoc:24014              

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 Abstract: The mini-superspace quantization of D=11 supergravity is equivalent to the quantization of a E10/K(E10) coset space sigma model, when the latter is restricted to the E10 Cartan subalgebra. As a consequence, the wavefunctions solving the relevant mini-superspace Wheeler-DeWitt equation involve automorphic (Maass wave) forms under the modular group W^+(E10)=PSL(2,O). Using Dirichlet boundary conditions on the billiard domain a general inequality for the Laplace eigenvalues of these automorphic forms is derived, entailing a wave function of the universe that is generically complex and always tends to zero when approaching the initial singularity. The significance of these properties for the nature of singularities in quantum cosmology in comparison with other approaches is discussed. The present approach also offers interesting new perspectives on some long standing issues in canonical quantum gravity.

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 Dates: 2010-02-172011-05
 Publication Status: Published in print
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 Identifiers: eDoc: 441587
Other: arXiv:0912.0854
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Title: Foundations of Space and Time: Reflections on Quantum Gravity
Source Genre: Book
 Creator(s):
Murugan, Jeff 1, Editor
Weltman, Amanda 1, Editor
Ellis, George F. R. 1, Author
Affiliations:
1 University of Cape Town, escidoc:persistent22            
Publ. Info: Cambridge : Cambridge University Press
Pages: - Volume / Issue: - Sequence Number: 6 Start / End Page: - Identifier: ISBN: 9780521114400