Wave Function of the Universe and Its Meaning

TL;DR

This paper develops a quantum cosmology framework for FRW spacetimes with scalar fields, establishing a Hilbert space structure, observables, and probabilistic interpretation using pseudo-Hermitian operator theory.

Contribution

It introduces a novel approach to quantum cosmology by applying pseudo-Hermitian operators to define the wave function of the universe with a clear probabilistic meaning.

Findings

Constructed a Hilbert space for the Wheeler-DeWitt solutions

Defined observables and physical wave functions with probabilistic interpretation

Proposed a formulation for the dynamics of the universe in quantum terms

Abstract

For a FRW-spacetime coupled to an arbitrary real scalar field, we endow the solution space of the associated Wheeler-DeWitt equation with a Hilbert-space structure, construct the observables, and introduce the physical wave functions of the universe that admit a genuine probabilistic interpretation. We also discuss a proposal for the formulation of the dynamics. The approach to quantum cosmology outlined in this article is based on the results obtained within the theory of pseudo-Hermitian operators.