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

TL;DR

This work studies inflationary fluctuations within the Effective Field Theory framework when the Goldstone mode $\pi$ has an approximate discrete shift symmetry, a setup realized in Axion Monodromy. Background oscillations generate oscillatory features in the power spectrum and resonance-driven, oscillatory non-Gaussianities across higher-point functions. The authors show that, under the EFT's validity and naturalness constraints, the 2-point function provides the dominant observable signal, with higher-point signals suppressed except for a narrow folded-shape region near the unitarity bound. They extend the analysis to oscillating couplings and mode-function corrections, derive the scaling with the resonance parameter $\alpha=\omega/H$, and identify unitarity-based limits that cap the observable non-Gaussianities while predicting a distinctive, testable oscillatory signature in cosmological data.

Abstract

We apply the Effective Field Theory of Inflation to study the case where the continuous shift symmetry of the Goldstone boson πis 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.

Figures (5)

• Figure 1: Explicit expression for ${\mathcal{I}}_{\rm I}^{(2)}$ for $\alpha=100$ and the approximations (\ref{['tricky']},\ref{['rightap']}) for large and small $y_1$ correspondingly.
• Figure 2: The shape of non-gaussian signal ( \ref{['3_point']}) induced by vertex $\dot\pi^3$ plotted for $\alpha=50$ away from the folded limit as a function of $x_i=k_i/k_1$.
• Figure 3: The shape of non-gaussian signal for the 3-point function generated by the vertex $\dot\pi(\partial_i\pi)^2$ ( \ref{['pidotgradpi']}) plotted for $\alpha=100$ away from the folded limit.
• Figure 4: Ratio of the signal to noise ratio for the 3-point function generated by vertex $\dot\pi^3$ (\ref{['3_point']}, \ref{['3p_fold']}) to the signal to noise ratio of the resonant correction to the 2-point function ( \ref{['2pt']}) plotted as a function of $\alpha$ for $c_s=0.5$ on the left, and $c_s=0.1$ on the right. The shaded region corresponds to the values of $\alpha$ where the effective theory breaks down, and the allowed values of $\alpha$ should be well within the white region. We see that the region where the signal to noise from the 3-point function is bigger than the signal to noise from the 2-point function is irrelevantly small and corresponds to when the theory is not under parametric control.
• Figure 5: Clockwise from top left we have plotted the cosine with local, equilateral and orthogonal shapes, in the valid range of $\alpha$. We see that as $\alpha$ becomes large, the cosine goes to zero.