Perturbation spectrum in inflation with cutoff

TL;DR

The paper investigates trans-Planckian modifications to the inflationary perturbation spectrum by implementing a natural ultraviolet cutoff through deformed commutation relations. Using an oscillator-variable formulation and adiabatic analysis, it shows that non-adiabatic effects are brief and that the horizon-crossing amplitude is preserved to $O(\sigma^2)$ with $\sigma = \sqrt{\beta} H$, leading to essentially unchanged spectra in de Sitter backgrounds; scaling arguments further confirm exact de Sitter invariance despite the cutoff, while non-de Sitter settings can introduce small cutoff-induced scale dependence. The results suggest that Planck-scale physics can imprint on the CMB only if the cutoff scale $\Delta x_{min}$ is not far below the horizon during inflation, and they discuss potential initial-condition mechanisms at the Planck time that might deterministically lead to the adiabatic vacuum.

Abstract

It has been pointed out that the perturbation spectrum predicted by inflation may be sensitive to a natural ultraviolet cutoff, thus potentially providing an experimentally accessible window to aspects of Planck scale physics. A priori, a natural ultraviolet cutoff could take any form, but a fairly general classification of possible Planck scale cutoffs has been given. One of those categorized cutoffs, also appearing in various studies of quantum gravity and string theory, has recently been implemented into the standard inflationary scenario. Here, we continue this approach by investigating its effects on the predicted perturbation spectrum. We find that the size of the effect depends sensitively on the scale separation between cutoff and horizon during inflation.