Quantum Cosmology of Generalized Two--Dimensional Dilaton Gravity Models

TL;DR

This paper explores quantum cosmology in two-dimensional dilaton gravity models, providing exact solutions, extending to supersymmetric cases, and discussing third-quantization applications.

Contribution

It introduces a mapping of these models to a constrained oscillator system and derives new exact solutions, including supersymmetric extensions.

Findings

Exact solutions to Wheeler-DeWitt equations are obtained.

A broader class of solvable minisuperspace models is identified.

Supersymmetric extensions and third-quantization discussions are included.

Abstract

The quantum cosmology of two-dimensional dilaton-gravity models is investigated. A class of models is mapped onto the constrained oscillator-ghost-oscillator model. A number of exact and approximate solutions to the corresponding Wheeler-DeWitt equation are presented. A wider class of minisuperspace models that can be solved in this fashion is identified. Supersymmetric extensions to the induced gravity theory and the bosonic string theory are then considered and closed-form solutions to the associated quantum constraints are derived. The possibility of applying the third-quantization procedure to two-dimensional dilaton-gravity is briefly discussed.