Notes on Dilaton Quantum Cosmology

TL;DR

This paper discusses the canonical quantization of homogeneous and isotropic dilaton cosmological models from string theory, focusing on conceptual issues like the problem of time and boundary conditions in quantum cosmology.

Contribution

It provides an analysis of the Hamiltonian formulation and quantization challenges specific to dilaton cosmology models derived from string theory.

Findings

Addressed the problem of time in quantum cosmology.

Analyzed the symmetry under clock reversals.

Discussed boundary conditions for the Wheeler-DeWitt equation.

Abstract

In these notes we address the canonical quantization of the cosmological models which appear as solutions of the low energy effective action of closed bosonic string theory (dilaton models). The analysis is restricted to the quantization of the minisuperspace models given by homogeneous and isotropic cosmological solutions. We study the different conceptual and technical problems arising in the Hamiltonian formulation of these models as a consequence of the presence of the so called Hamiltonian constraint. In particular we address the problem of time in quantum cosmology, the characterization of the symmetry under clock reversls arising from the existence of a Hamiltonian constraint, and the problem of inposing boundary conditions on the space of solutions of the Wheeler-DeWitt equation.