  In this paper we investigate to which extent noncommutativity, a
intrinsically quantum property, may influence the Friedmann-Robertson-Walker
cosmological dynamics at late times/large scales. To our purpose it will be
enough to explore the asymptotic properties of the cosmological model in the
phase space. Our recipe to build noncommutativity into our model is based in
the approach of reference [Phys. Rev. Lett. {\bf 88} (2002) 161301], and can be
summarized in the following steps: i) the Hamiltonian is derived from the
Einstein-Hilbert action (plus a self-interacting scalar field action) for a
Friedmann-Robertson-Walker spacetime with flat spatial sections, ii) canonical
quantization recipe is applied, i. e., the minisuperspace variables are
promoted to operators, and the WDW equation is written in terms of these
variables, iii) noncommutativity in the minisuperspace is achieved through the
replacement of the standard product of functions by the Moyal star product in
the WDW equation, and, finally, iv) semi-classical cosmological equations are
obtained by means of the WKB approximation applied to the (equivalent) modified
Hamilton-Jacobi equation. We demonstrate, indeed, that noncommutative effects
of the kind considered here, can be those responsible for the present speed up
of the cosmic expansion.
