Large n -point functions in resonant inflation

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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 ω exceeds the naive cutoff of the theory, 4 π f . However, as noted by Hook and Rattazzi [1], 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 ≲ n ≲ 9 are potentially observable. In this regime, the signal exhibits 350–1000 oscillations per decade in k .

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