(Non)commutative isotropization in Bianchi I with Barotropic perfect fluid and $\Lambda$ Cosmological

TL;DR

This paper explores classical solutions in Bianchi I cosmology with perfect fluid and cosmological constant, analyzing how noncommutativity affects isotropization and suggesting additional matter components may be needed for full isotropization.

Contribution

It introduces a noncommutative framework in Bianchi I models and examines its impact on anisotropy evolution, highlighting the need for extra matter types for complete isotropization.

Findings

Noncommutativity influences anisotropic parameters over time.

Anisotropic parameters tend to constant curvature in noncommutative scenarios.

Additional matter like dark energy may be required for full isotropization.

Abstract

We present the classical solutions to the Einstein field equations derived using the WKB-like and Hamilton procedures. The investigation is carried out in the commutative and noncommutative scenario for the Bianchi type I cosmological model coupled to barotropic perfect fluid and $\lambda $ Cosmological for two different gauges. Noncommutativity is achieved by modifying the symplectic structure considering that all minisuperspace variables $\rm q^i$ does not commute and by a deformation between all the minisuperspace variables. In the gauge N=1, it is possible to obtain that the anisotropic parameter $\rm \beta_{\pm nc}$ tend to a constant curvature for large period of time considering different values in the noncommutative parameters $\theta$ and cosmological term. However, this behavior give the idea that is necessary introduce other class of matter in the models, for to have a real isotropization in the model, such as dark energy or dark matter.