Non Commutative Bianchi type II Quantum Cosmology

TL;DR

This paper explores noncommutative quantum cosmological models of Bianchi type II, deriving solutions to the Wheeler-DeWitt equation with and without noncommutativity, revealing effects on anisotropic early universe models.

Contribution

It introduces a noncommutative framework for Bianchi type II cosmology and provides explicit quantum solutions for these models, extending previous commutative approaches.

Findings

Derived quantum solutions for noncommutative Bianchi type II models.

Showed how noncommutativity modifies the minisuperspace structure.

Compared commutative and noncommutative quantum cosmological solutions.

Abstract

In this paper we present the noncommutative Bianchi Class A cosmological models coupled to barotropic perfect fluid. The commutative and noncommutative quantum solution to the Wheeler-DeWitt equation for any factor ordering, to the anisotropic Bianchi type II cosmological model are found, using a stiff fluid ($\gamma=1$). In our toy model, we introduce noncommutative scale factors, is say, we consider that all minisuperspace variables $\rm q^i$ does not commute, so the simplectic structure was modified.