Trans-Planckian Effects in Inflationary Cosmology and the Modified Uncertainty Principle

TL;DR

This paper explores how a modified uncertainty principle with a minimum length affects inflationary cosmology, leading to non-linear dispersion relations and damping of high-energy fluctuations, which influence the initial conditions of density perturbations.

Contribution

It implements a minimum length scale into scalar field theory during inflation, deriving non-linear dispersion relations and analyzing their impact on fluctuation spectra.

Findings

Emergence of Unruh-type dispersion relations

Damping of trans-Planckian fluctuations

Initial fluctuation spectrum tends to be flat

Abstract

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.