Wave Function of the Universe and Its Meaning
Ali Mostafazadeh

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.
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