Billiard Representation for Multidimensional Quantum Cosmology near the Singularity

TL;DR

This paper analyzes multidimensional quantum cosmological models near singularities, showing their dynamics can be represented as billiards in Lobachevsky space, and provides solutions to the Wheeler-DeWitt equation in this regime.

Contribution

It introduces a billiard representation for cosmological models near singularities and proposes a third-quantized framework based on this approach.

Findings

Dynamics near singularity reduces to billiard motion in Lobachevsky space

Wheeler-DeWitt equation is solved asymptotically in this regime

A third-quantized model is proposed

Abstract

The degenerate Lagrangian system describing a lot of cosmological models is considered. When certain restrictions on the parameters of the model are imposed, the dynamics of the model near the "singularity" is reduced to a billiard on the Lobachevsky space. The Wheeler-DeWitt equation in the asymptotical regime is solved and a third-quantized model is suggested.