  We study the importance of lattice refinement in achieving a successful
inflationary era. We solve, in the continuum limit, the second order difference
equation governing the quantum evolution in loop quantun cosmology, assuming
both a fixed and a dynamically varying lattice in a suitable refinement model.
We thus impose a constraint on the potential of a scalar field, so that the
continuum approximation is not broken. Considering that such a scalar field
could play the role of the inflaton, we obtain a second constraint on the
inflationary potential so that there is consistency with the CMB data on large
angular scales. For a $m^2\phi^2/2$ inflationary model, we combine the two
constraints on the inflaton potential to impose an upper limit on $m$, which is
severely fine-tuned in the case of a fixed lattice. We thus conclude that
lattice refinement is necessary to achieve a natural inflationary model.
