  There are good indications that fundamental physics gives rise to a modified
space-momentum uncertainty relation that implies the existence of a minimum
length scale. We implement this idea in the scalar field theory that describes
density perturbations in flat Robertson-Walker space-time. This leads to a
non-linear time-dependent dispersion relation that encodes the effects of
Planck scale physics in the inflationary epoch. Unruh type dispersion relations
naturally emerge in this approach, while unbounded ones are excluded by the
minimum length principle. We also find red-shift induced modifications of the
field theory, due to the reduction of degrees of freedom at high energies, that
tend to dampen the fluctuations at trans-Planckian momenta. In the specific
example considered, this feature helps determine the initial state of the
fluctuations, leading to a flat power spectrum.
