(Non)commutative isotropization in Bianchi i with barotropic perfect fluid and Λ cosmological

Abstract

Using the WKB-like and Hamilton procedures classical solutions to commutative and noncommutative cosmology are found. This is carried out in the Bianchi type I cosmological model coupled to barotropic perfect fluid and cosmological constant. Noncommutativity is achieved by modifying the symplectic structure considering that minisuperspace variables do not commute, using a deformation between all the minisuperspace variables. It is shown that the anisotropic parameter β ±nc for some value in the Λ cosmological term and noncommutative θ parameter, present a dynamical isotropization until a critical cosmic time t c . After this time the effects of minisuperspace noncommutativity in the isotropization seem to disappear. © 2007 Springer Science+Business Media, LLC.