Cosmological quantum billiards
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.
Keywords
Cite
@article{arxiv.0912.0854,
title = {Cosmological quantum billiards},
author = {Axel Kleinschmidt and Hermann Nicolai},
journal= {arXiv preprint arXiv:0912.0854},
year = {2010}
}
Comments
18 pages. Based on a talk by H. Nicolai in honor of George Ellis' 70th birthday. v2: reference added. v3: reference added