  Loop quantum cosmology of the k=0 FRW model (with a massless scalar field) is
shown to be exactly soluble if the scalar field is used as the internal time
already in the classical Hamiltonian theory. Analytical methods are then used
i) to show that the quantum bounce is generic; ii) to establish that the matter
density has an absolute upper bound which, furthermore, equals the critical
density that first emerged in numerical simulations and effective equations;
iii) to bring out the precise sense in which the Wheeler DeWitt theory
approximates loop quantum cosmology and the sense in which this approximation
fails; and iv) to show that discreteness underlying LQC is fundamental.
Finally, the model is compared to analogous discussions in the literature and
it is pointed out that some of their expectations do not survive a more careful
examination. An effort has been made to make the underlying structure
transparent also to those who are not familiar with details of loop quantum
gravity.
