Loop quantum cosmology and the Wheeler–De Witt equation

We present some results concerning the large volume limit of loop quantum cosmology in the flat homogeneous and isotropic case. We derive the Wheeler–De Witt equation in this limit. Looking for the action from which this equation can also be obtained, we then address the problem of the modifications to be brought to the Friedman’s equation and to the equation of motion of the scalar field, in the classical limit.