Non commutative classical and Quantum fractionary Cosmology: Anisotropic Bianchi Type I case

TL;DR

This paper investigates the impact of non-commutativity on fractional classical and quantum Bianchi Type I cosmology with a scalar field, revealing modifications in symplectic structure and quantum probability density.

Contribution

It introduces non-commutative variables into fractional cosmology models, modifying the symplectic structure and analyzing quantum probability density changes.

Findings

Modified symplectic structure due to non-commutativity.

Quantum probability density shows new structure with non-commutative parameter.

Alterations in classical and quantum dynamics of Bianchi Type I model.

Abstract

In this work, we will explore the effects of non-commutativity in fractional classical and quantum schemes using the anisotropicc Bianchi Type I cosmological model coupled to a scalar field in the K-essence formalism. We introduce non-commutative variables considering that all minisuperspace variables $q^i_{nc}$ do not commute, so the symplectic structure was modified, resulting in some changes with respect to the traditional formalism. In the quantum regime, the probability density presents a new structure in the scalar field corresponding to the value of the non-commutative parameter.