Noncommutative cosmological model in the presence of a phantom fluid

We study noncommutative classical Friedmann-Robertson-Walker cosmological models. The constant curvature of the spatial sections can be positive (k = 1), negative (k = -1) or zero (k = 0). The matter is represented by a perfect fluid with negative pressure, phantom fluid, which satisfies the equation of state p = alpha rho, with alpha < -1, where p is the pressure and rho is the energy density. We use Schutz's formalism in order to write the perfect fluid Hamiltonian. The noncommutativity is introduced by nontrivial Poisson brackets between few variables of the models. In order to recover a description in terms of commutative variables, we introduce variables transformations that depend on a noncommutative parameter (gamma). The main motivation for the introduction of the noncommutativity is trying to explain the present accelerated expansion of the universe. We obtain the dynamical equations for these models and solve them. The solutions have four constants: gamma, a parameter associated with the fluid energy C, k, alpha and the initial conditions of the models variables. For each value of a, we obtain different equations of motion. Then, we compare the evolution of the universe in the noncommutative models with the corresponding commutative ones (gamma -> 0). The results show that gamma is very useful for describing an accelerating universe. We also obtain estimates for the noncommutative parameter gamma. Then, using those values of gamma, in one of the noncommutative cosmological models with a specific value of alpha, we compute the amount of time those universes would take to reach the big rip.