Quantum cosmology with scalar fields: self-adjointness and cosmological scenarios

TL;DR

This paper examines unitarity in quantum cosmological models with scalar fields, demonstrating conditions for self-adjoint Hamiltonians and the occurrence of non-singular bounces, highlighting the importance of unitarity in quantum cosmology.

Contribution

It analyzes self-adjointness and unitarity in quantum cosmology with scalar fields using Schutz's formalism, identifying conditions for unitary evolution and extensions for non-self-adjoint cases.

Findings

Unitary evolution depends on factor ordering and measure choices.

Self-adjoint extensions exist for certain Hamiltonians.

Non-singular bounce occurs even without strict unitarity.

Abstract

We discuss the issue of unitarity in particular quantum cosmological models with scalar field. The time variable is recovered, in this context, by using the Schutz's formalism for a radiative fluid. Two cases are considered: a phantom scalar field and an ordinary scalar field. For the first case, it is shown that the evolution is unitary provided a convenient factor ordering and inner product measure are chosen; the same happens for the ordinary scalar field, except for some special cases for which the Hamiltonian is not self-adjoint but admits a self-adjoint extension. In all cases, even for those cases not exhibiting unitary evolution, the formal computation of the expectation value of the scale factor indicates a non-singular bounce. The importance of the unitary evolution in quantum cosmology is briefly discussed.