Supersymmetric quantum cosmological billiards

TL;DR

This paper explores the quantum behavior of cosmological models near singularities using supersymmetric supergravity and automorphic forms, revealing that the universe's wavefunction tends to zero at the initial singularity, with implications for quantum cosmology.

Contribution

It introduces a novel quantization approach of supergravity billiards using automorphic forms and analyzes the wavefunction's behavior near singularities.

Findings

Wavefunctions involve automorphic (Maass wave) forms under the modular group.

The wavefunction of the universe tends to zero approaching the singularity.

A general inequality constrains the Laplace eigenvalues of automorphic forms.

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.