Deformed phase space in a two-dimensional minisuperspace model

We study the effects of noncommutativity and deformed Heisenberg algebra on the evolution of a two-dimensional minisuperspace cosmological model in classical and quantum regimes. The phase-space variables turn out to correspond to the scale factor of a flat FRW model with a positive cosmological constant and a dilatonic field with which the action of the model is augmented. The exact classical and quantum solutions in commutative and noncommutative cases are presented. We also obtain some approximate analytical solutions for the corresponding classical and quantum cosmology in the presence of the deformed Heisenberg relations between the phase-space variables, in the limit where the minisuperspace variables are small. These results are compared with the standard commutative and noncommutative cases, and similarities and differences of these solutions are discussed.