Minimal modifications of the primordial power spectrum from an adiabatic short distance cutoff

TL;DR

This paper models how an adiabatic cutoff at high energies during inflation can cause small, oscillatory modifications to the primordial power spectrum, providing a potential lower bound for such deviations.

Contribution

It introduces a simple model linking a high-energy cutoff to specific oscillations in the primordial power spectrum, expressed in terms of H/M and slow roll parameters.

Findings

Oscillations in the power spectrum are proportional to (H/M)^3.

Derived a formula relating oscillation amplitude and frequency to the cutoff scale.

Small oscillations set a lower bound on primordial spectrum modifications.

Abstract

As a simple model for unknown Planck scale physics, we assume that the quantum modes responsible for producing primordial curvature perturbations during inflation are placed in their instantaneous adiabatic vacuum when their proper momentum reaches a fixed high energy scale M. The resulting power spectrum is derived and presented in a form that exhibits the amplitude and frequency of the superimposed oscillations in terms of H/M and the slow roll parameter epsilon. The amplitude of the oscillations is proportional to the third power of H/M. We argue that these small oscillations give the lower bound of the modifications of the power spectrum if the notion of free mode propagation ceases to exist above the critical energy scale M.