Scalar field quantum cosmology: a Schr\"{o}dinger picture

TL;DR

This paper introduces a canonical transformation in scalar field FRW cosmology to define a time parameter, leading to a Schrödinger-like equation for quantum cosmology and exploring quantum corrections to classical solutions.

Contribution

It presents a novel canonical transformation approach that identifies a time parameter and derives a Schrödinger-Wheeler-DeWitt equation in scalar field quantum cosmology.

Findings

Classical solutions obtained in terms of the new time parameter.

Quantum wave functions constructed for the universe.

Quantum effects analyzed using many-worlds and ontological interpretations.

Abstract

We study the classical and quantum models of a scalar field Friedmann-Robertson-Walker (FRW) cosmology with an eye to the issue of time problem in quantum cosmology. We introduce a canonical transformation on the scalar field sector of the action such that the momentum conjugate to the new canonical variable appears linearly in the transformed Hamiltonian. Using this canonical transformation, we show that, it may lead to the identification of a time parameter for the corresponding dynamical system. In the cases of flat, closed and open FRW universes the classical cosmological solutions are obtained in terms of the introduced time parameter. Moreover, this formalism gives rise to a Schr\"{o}dinger-Wheeler-DeWitt equation for the quantum-mechanical description of the model under consideration, the eigenfunctions of which can be used to construct the wave function of the universe. We use the resulting wave functions in order to investigate the possible corrections to the classical cosmologies due to quantum effects by means of the many-worlds and ontological interpretation of quantum cosmology.