A first step towards the inflationary trans-Planckian problem treatment in loop quantum 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 paper we demonstrate that the usual predictions of inflation for the spectrum of cosmological fluctuations do indeed depend 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 show that in some cases important deviations from the usual predictions of inflation are obtained. Some implications of this result for the unification of fundamental physics and early Universe cosmology are discussed.

The goal of this article is to provide an overview of the current state of the art in loop quantum cosmology for three sets of audiences: young researchers interested in entering this area; the quantum gravity community in general; and, cosmologists who wish to apply loop quantum cosmology to probe modifications in the standard paradigm of the early universe. An effort has been made to streamline the material so that, as described at the end of section I, each of these communities can read only the sections they are most interested in, without a loss of continuity.

The naive calculation of black hole evaporation makes the thermal emission depend on the arbitrary high frequency behaviour of the theory where the theory is certainly wrong. Using the sonic analog to black holes-- dumb holes-- I show numerically that a change in the dispersion relation at high frequencies does not seem to alter the evaporation process, lending weight to the reality of the black hole evaporation process. I also suggest a reason for the insensitivity of the process to high frequency regime.