Scalar field in the Bianchi I: Non commutative classical and Quantum Cosmology

TL;DR

This paper explores classical and quantum solutions in a Bianchi I cosmological model with a scalar field, incorporating noncommutative geometry, revealing effects like isotropization and modified wave functions due to noncommutativity.

Contribution

It provides exact classical and quantum solutions for a noncommutative Bianchi I model with a scalar field, extending minisuperspace formalism to include noncommutative variables.

Findings

Noncommutative parameters induce isotropization up to a critical time.

Wave function structure is altered by noncommutativity.

Classical solutions show dynamical isotropization influenced by noncommutative effects.

Abstract

Using the ADM formalism in the minisuperspace, we obtain the commutative and noncommutative exact classical solutions and exact wave function to the Wheeler-DeWitt equation with an arbitrary factor ordering, for the anisotropic Bianchi type I cosmological model, coupled to a scalar field, cosmological term and barotropic perfect fluid. We introduce noncommutative scale factors, considering that all minisuperspace variables $\rm q^i$ do not commute, so the symplectic structure was modified. In the classical regime, it is shown that the anisotropic parameter $\rm \beta_{\pm nc}$ and the field $\phi$, for some value in the $\lambda_{eff}$ cosmological term and noncommutative $\theta$ parameter, present a dynamical isotropization up to a critical cosmic time $t_{c}$; after this time, the effects of isotropization in the noncommutative minisuperspace seems to disappear. In the quantum regimen, the probability density presents a new structure that corresponds to the value of the noncommutativity parameter.