  In the present work, we study the dynamical evolution of an homogeneous and
anisotropic, noncommutative (NC) Bianchi I (BI) model coupled to a radiation
perfect fluid. Our first motivation is determining if the present model tends
to an homogeneous and isotropic NC Friedmann-Robertson-Walker (FRW) model,
during its evolution. In order to simplify our task, we use the Misner
parametrization of the BI metric. In terms of that parametrization the BI
metric has three metric functions: the scale factor $a(t)$ and the two
parameters $\beta_\pm (t)$, which measure the spatial anisotropy of the model.
Our second motivation is trying to describe the present accelerated expansion
of the universe using noncommutativity (NCTY). The NCTY is introduced by two
nontrivial Poisson brackets between some geometrical as well as matter
variables of the model. We recover the description in terms of commutative
variables by introducing some variables transformations that depend on the NC
parameter. Using those variables transformations, we rewrite the total NC
Hamiltonian of the model in terms of commutative variables. From the resulting
Hamiltonian, we obtain the dynamical equations for a generic perfect fluid. In
order to solve these equations, we restrict our attention to a model where the
perfect fluid is radiation. We solve, numerically, these equations and compare
the NC solutions to the corresponding commutative ones. The comparison shows
that the NC model may be considered as a possible candidate for describing the
accelerated expansion of the universe. Finally, we obtain estimates for the NC
parameter and compare the main results of the NC BI model coupled to radiation
with the same NC BI model coupled to other perfect fluids. As our main result,
we show that the solutions, after some time, produce an isotropic universe.
