Can noncommutative effects account for the present speed up of the cosmic expansion?

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.