Cosmological scenarios in quantum cosmology of Brans-Dicke theory of gravity on Einstein and Jordan frames

TL;DR

This paper investigates the quantum cosmology of Brans-Dicke theory in Einstein and Jordan frames, analyzing the self-adjointness of the Hamiltonian and its implications for universe evolution scenarios.

Contribution

It provides a detailed analysis of the self-adjointness of the Hamiltonian in Brans-Dicke quantum cosmology and explores the equivalence of Einstein and Jordan frames.

Findings

Cosmological scenarios are weakly dependent on self-adjointness conditions.

Specific ordering parameters are required for frame equivalence.

Wave-function solutions are obtained for universe evolution predictions.

Abstract

The Hamiltonian of any quantum cosmological model must obey some conditions in order to be self-adjoint, or to admit self-adjoint extensions. We will consider in this paper the self-adjoint character of the Hamiltonian resulting from the Brans-Dicke theory, both in Einstein and Jordan frames. In both cases we find the wave-function solutions in order to obtain concrete predictions for the evolution of the Universe. We show that the specific cosmological scenarios obtained depend very weakly on the conditions of having a self-adjoint operator. The problem of equivalence between Einstein and Jordan frames is considered, and it is shown that this equivalence implies a specific ordering parameter, as well as a particular choice of the physical variables.