Canonical measure and the flatness of a FRW universe

We consider the claim of Hawking and Page that the canonical measure applied to Friedmann--Robertson--Walker models with a massive scalar field can solve the flatness problem, i.e. , regardless of inflation occurring or not. We point out a number of ways in which this prediction, which relies predominantly on post-Planckian regions of the classical phase space, could break down. By considering a general potential we are able to understand how the ambiguity for found by Page in the -theory is present, in general, for scalar field models when the potential is bounded from above. We suggest reasons why such potentials are more realistic, which then results in the value of being arbitrary. Although the canonical measure gives an ambiguity (due to the infinite measure over arbitrary scale factors) for the possibility of inflation, the inclusion of an input from quantum cosmology could resolve this ambiguity. This could simply be that due to a `quantum event' the Universe started small, and provided a suitable scalar potential is present an inflationary period could then be `near certain' to proceed in order to set infinitesimally close to unity. We contrast the measure obtained in this way with the more usual ones obtained in quantum cosmology: the Hartle--Hawking and tunnelling ones.