Dilaton cosmology, noncommutativity, and generalized uncertainty principle

The effects of noncommutativity and of the existence of a minimal length on the phase space of a dilatonic cosmological model are investigated. The existence of a minimum length results in the generalized uncertainty principle (GUP), which is a deformed Heisenberg algebra between the minisuperspace variables and their momenta operators. I extend these deformed commutating relations to the corresponding deformed Poisson algebra. For an exponential dilaton potential, the exact classical and quantum solutions in the commutative and noncommutative cases, and some approximate analytical solutions in the case of GUP, are presented and compared