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We study the importance of lattice refinement in achieving a successfulinflationary era. We solve, in the continuum limit, the second order differenceequation governing the quantum evolution in loop quantun cosmology, assumingboth 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 thecontinuum approximation is not broken. Considering that such a scalar fieldcould play the role of the inflaton, we obtain a second constraint on theinflationary potential so that there is consistency with the CMB data on largeangular scales. For a $m^2\phi^2/2$ inflationary model, we combine the twoconstraints on the inflaton potential to impose an upper limit on $m$, which isseverely fine-tuned in the case of a fixed lattice. We thus conclude thatlattice refinement is necessary to achieve a natural inflationary model.

Lattice Refining Loop Quantum Cosmology and Inflation