Near-singularity Wheeler-DeWitt wavefunctions for 5d BKL dynamics are shown to correspond to Hecke L-functions over Gaussian or Eisenstein integers, whose Euler products define complex 'primon gas' partition functions.
Supersymmetric quantum cosmological billiards
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abstract
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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Wheeler-DeWitt wavefunctions for 5d BKL dynamics, automorphic L-functions and complex primon gases
Near-singularity Wheeler-DeWitt wavefunctions for 5d BKL dynamics are shown to correspond to Hecke L-functions over Gaussian or Eisenstein integers, whose Euler products define complex 'primon gas' partition functions.