  Due to the tremendous red-shift that occurs during the inflationary epoch in
the early universe, it has been realized that trans-Planckian physics may
manifest itself at energies much lower than the Planck energy. The presence of
a fundamental scale suggests that local Lorentz invariance may be violated at
sufficiently high energies. Motivated by this possibility, recently, different
models that violate Lorentz invariance locally have been used to evaluate the
trans-Planckian corrections to the inflationary density perturbation spectrum.
However, certain astrophysical observations seem to indicate that local Lorentz
invariance may be preserved to extremely high energies. In such a situation, to
study the trans-Planckian effects, it becomes imperative to consider models
that preserve local Lorentz invariance even as they contain a fundamental
scale. In this work, we construct one such model and evaluate the resulting
spectrum of density perturbations in the power-law inflationary scenario. While
our model reproduces the standard spectrum on small scales, it naturally
predicts a suppression of power on large scales. In fact, the spectrum we
obtain has some features which are similar to the one that has recently been
obtained from non-commutative inflation. However, we find that the amount of
suppression predicted by our model is far less than that is required to fit the
observations. We comment on the fact that, with a suitable choice of initial
conditions, our approach can lead to corrections at the infra-red as well as at
the ultra-violet ends of the spectrum.
