Quantum cosmology of scalar-tensor theories and self-adjointness

TL;DR

This paper investigates the self-adjointness of quantum Hamiltonians derived from scalar-tensor theories, specifically Brans-Dicke models, using mathematical criteria to determine their self-adjoint extensions and physical viability.

Contribution

It provides a detailed analysis of the self-adjointness conditions for quantum minisuperspace Hamiltonians in Brans-Dicke theories, including criteria for suitable self-adjoint extensions.

Findings

Identifies conditions for Hamiltonian self-adjointness in scalar-tensor quantum cosmology

Determines when self-adjoint extensions are necessary and physically appropriate

Uses von Neumann theorem and Laplacian analogy for analysis

Abstract

In this paper, the problem of the self-adjointness for the case of a quantum minisuperspace Hamiltonian retrieved from a Brans-Dicke (BD) action is investigated. Our matter content is presented in terms of a perfect fluid, onto which the Schutz's formalism will be applied. We use the von Neumann theorem and the similarity with the Laplacian operator in one of the variables to determine the cases where the Hamiltonian is self-adjoint and if it admits self-adjoint extensions. For the latter, we study which extension is physically more suitable.