(Small) Resonant non-Gaussianities: Signatures of a Discrete Shift Symmetry in the Effective Field Theory of Inflation

TL;DR

This paper explores how a discrete shift symmetry during inflation causes oscillations in the CMB power spectrum and non-Gaussianities, with potential for detection in the 2-point function and higher correlations as a consistency check.

Contribution

It extends the Effective Field Theory of Inflation to include discrete shift symmetries, analyzing their impact on oscillatory signatures in correlation functions.

Findings

Oscillations primarily appear in the 2-point function.

Higher-order correlations show smaller oscillatory signals.

Detection of oscillations in the 2-point function is more feasible.

Abstract

We apply the Effective Field Theory of Inflation to study the case where the continuous shift symmetry of the Goldstone boson \pi is softly broken to a discrete subgroup. This case includes and generalizes recently proposed String Theory inspired models of Inflation based on Axion Monodromy. The models we study have the property that the 2-point function oscillates as a function of the wavenumber, leading to oscillations in the CMB power spectrum. The non-linear realization of time diffeomorphisms induces some self-interactions for the Goldstone boson that lead to a peculiar non-Gaussianity whose shape oscillates as a function of the wavenumber. We find that in the regime of validity of the effective theory, the oscillatory signal contained in the n-point correlation functions, with n>2, is smaller than the one contained in the 2-point function, implying that the signature of oscillations, if ever detected, will be easier to find first in the 2-point function, and only then in the higher order correlation functions. Still the signal contained in higher-order correlation functions, that we study here in generality, could be detected at a subleading level, providing a very compelling consistency check for an approximate discrete shift symmetry being realized during inflation.