Trans-Planckian problem of inflationary cosmology

In most current models of inflation based on a weakly self-coupled scalar matter field minimally coupled to gravity, the period of inflation lasts so long that, at the beginning of the inflationary period, the physical wavelengths of comoving scales which correspond to the present large-scale structure of the Universe were smaller than the Planck length. Thus, the usual computations of the spectrum of fluctuations in these models involve extrapolating low-energy physics (both in the matter and gravitational sector) into regions where this physics is not applicable. In this article we study the dependence of the usual predictions of inflation for the spectrum of cosmological fluctuations on the hidden assumptions about super-Planck scale physics. We introduce a class of modified dispersion relations to mimic possible effects of super-Planck scale physics, and find that, given an initial state determined by minimizing the energy density, for dispersions relations introduced by Unruh the spectrum is unchanged, whereas for a class of dispersion relations similar to those used by Corley and Jacobson (which involve a more radical departure from the usual linear relation) important deviations from the usual predictions of inflation can be obtained. Some implications of this result for the unification of fundamental physics and early Universe cosmology are discussed.