Dilaton Quantum Cosmology in Two Dimensions

TL;DR

This paper explores a two-dimensional dilaton gravity model as a simplified quantum cosmology framework, analyzing classical solutions, quantum corrections, and the Wheeler-DeWitt equation to understand singularities and quantum states of the universe.

Contribution

It introduces a renormalizable 2D dilaton gravity model for quantum cosmology, examining quantum backreaction effects and singularity formation within this simplified setting.

Findings

Quantum corrections can create new singularities at low matter densities.

Singularities may occur in quantum regions where classical spacetime notions break down.

The Wheeler-DeWitt equation solutions depend on the quantum state, affecting singularity appearance.

Abstract

We consider a renormalizable two-dimensional model of dilaton gravity coupled to a set of conformal fields as a toy model for quantum cosmology. We discuss the cosmological solutions of the model and study the effect of including the backreaction due to quantum corrections. As a result, when the matter density is below some threshold new singularities form in a weak coupling region, which suggests that they will not be removed in the full quantum theory. We also solve the Wheeler-DeWitt equation. Depending on the quantum state of the Universe, the singularities may appear in a quantum region where the wave function is not oscillatory, i.e., when there is not a well defined notion of classical spacetime.