Simple model of big-crunch/big-bang transition

TL;DR

This paper models the classical and quantum behavior of a test particle in a spacetime that contracts and expands, providing insights into the nature of cosmic singularities during the big-crunch/big-bang transition.

Contribution

It introduces a simple classical and quantum model of a particle in a contracting and expanding compactified spacetime to study cosmic singularities.

Findings

Quantum representation of particle observables is achieved.

Model offers insights into the nature of cosmic singularities.

Classical and quantum dynamics are explicitly formulated.

Abstract

We present classical and quantum dynamics of a test particle in the compactified Milne space. Background spacetime includes one compact space dimension undergoing contraction to a point followed by expansion. Quantization consists in finding a self-adjoint representation of the algebra of particle observables. Our model offers some insight into the nature of the cosmic singularity.