Large $n$-point Functions in Resonant Inflation

TL;DR

This paper explores a new inflationary regime where small, rapid oscillations in the potential lead to prominent higher-order non-Gaussianities, with observable signals in n-point functions for 3 to 9 points, exceeding the usual power spectrum focus.

Contribution

It introduces a novel inflationary regime with high-frequency oscillations causing dominant non-Gaussian signals in higher-order correlation functions, expanding the observable signatures beyond the power spectrum.

Findings

Higher-order n-point functions (n=3 to 9) show significant oscillatory signals.

Oscillation frequency exceeds the naive cutoff, leading to observable non-Gaussianities.

The regime predicts 350-1000 oscillations per decade in momentum space.

Abstract

We investigate a qualitatively new regime of inflationary models with small and rapid oscillations in the potential-resonant non-Gaussianity. In contrast to the standard scenario, where most of the observable information is encoded in the power spectrum, in this regime the oscillatory signal predominantly appears in higher-order correlation functions with large $n$. This behavior emerges when the oscillation frequency $\omega$ exceeds the naive cutoff of the theory, $4\pi f$. However, as noted by Hook and Rattazzi [2306.12489], the actual cutoff is somewhat higher -- though only logarithmically -- when the amplitude of the oscillations is small. We identify a phenomenologically relevant window in which $n$-point functions with $3 \lesssim n \lesssim 9$ are potentially observable. In this regime, the signal exhibits 350-1000 oscillations per decade in $k$.