On the Initial Singularity Problem in Two Dimensional Quantum Cosmology

TL;DR

This paper investigates the initial singularity in two-dimensional quantum cosmology, demonstrating that quantum effects can smooth classical singularities and challenge traditional big-bang concepts.

Contribution

It introduces a Liouville interaction with specific parameters ensuring algebra closure, and shows quantum effects eliminate classical singularities in the model.

Findings

Propagation amplitude vanishes at a=0, indicating singularity smoothing

The model is classically solvable with a general solution including the singularity

Quantum effects suggest the big-bang may be a classical extrapolation

Abstract

The problem of how to put interactions in two-dimensional quantum gravity in the strong coupling regime is studied. It shows that the most general interaction consistent with this symmetry is a Liouville term that contain two parameters $(\alpha, \beta)$ satisfying the algebraic relation $2\beta - \alpha =2$ in order to assure the closure of the diffeomorphism algebra. The model is classically soluble and it contains as general solution the temporal singularity. The theory is quantized and we show that the propagation amplitude fall tozero in $\tau =0$. This result shows that the classical singularities are smoothed by quantum effects and the bing-bang concept could be considered as a classical extrapolation instead of a physical concept.