Amplitude-real-phase exact solutions for quantum mixmaster universes

Abstract

We present a set of exact solutions for quantum Bianchi type-IX anisotropic cosmological models (including the Taub model) of the form Y = W e -S . These solutions are spread over all values of anisotropy near the singularity, but at larger values of the radius of the universe they are strongly peaked around the k = + 1 Friedmann-Robertson-Walker model.

Quintom Potential from Quantum Anisotropic Cosmological Models

“…This function was calculated explicitly for the diagonal Bianchi type IX model by Kodama, who also found Ψ A = const as a solution, and Ψ A is pure imaginary, for a certain factor ordering, one expects a solution of the form ψ = We ±Φ , where W is a constant, and Φ = iΦ A . In fact this type of solution has been found for the diagonal Bianchi Class A cosmological models [46,47], but W in some cases is a function, as we will see in our present study.…”

“…So, the quantum solutions for each potential scalar fields are presented in quadrature form, using the equations (46,54) and (57).…”

The Bohm Interpretation of Quantum Cosmology

“…Other authors have studied Bianchi IX models adopting other interpretations of quantum cosmology [52,53,54,55,56].…”

Cosmological Bianchi Class A Models in Sáez-Ballester Theory

“…similar solutions were given by Moncrief and Ryan (Moncrief & Ryan, 1991) in standard quantum cosmology in general relativity. In table 4 we present the superpotential function S, the amplitude of probability W and the relations between the parameters for the corresponding Bianchi Class A models.…”