A Consistency Relation for Single-Field Inflation with Power Spectrum Oscillations

TL;DR

This paper establishes a theoretical upper limit on the oscillation frequency of the scalar power spectrum in single-field inflation, linking phase variations, interactions, and perturbation theory validity.

Contribution

It derives a new upper bound on oscillation frequency in the power spectrum and connects phase changes with interaction strength, extending previous effective field theory constraints.

Findings

Derived an upper bound on oscillation frequency.

Linked phase variation to interaction strength.

Provided a method to constrain oscillations using higher-point correlations.

Abstract

We derive a theoretical upper bound on the oscillation frequency in the scalar perturbation power spectrum of single-field inflation. Oscillations are most naturally produced by modified vacua with varying phase. When this phase changes rapidly, it induces strong interactions between the scalar fluctuations. If the interactions are sufficiently strong the theory cannot be evaluated using perturbation theory, hence imposing a limit on the oscillation frequency. This complements the bound found by Weinberg governing the validity of effective field theory. The generalized consistency relation also allows one to use squeezed configurations of higher-point correlations to place constraints on the power spectrum oscillations.