Feeding your Inflaton: Non-Gaussian Signatures of Interaction Structure

TL;DR

This paper explores how different inflaton interactions produce distinct non-Gaussian signatures in the early universe, focusing on higher-order moments and their observational implications.

Contribution

It introduces a framework to distinguish interaction types by analyzing the scaling of higher-order moments in primordial non-Gaussianity.

Findings

Derived analytic expressions for Minkowski functionals and halo mass function based on moment structure.

Showed how different interaction classes can be observationally distinguished.

Clarified the theoretical distinction between near-Gaussianity and calculational control.

Abstract

Primordial non-Gaussianity is generated by interactions of the inflaton field, either self-interactions or couplings to other sectors. These two physically different mechanisms can lead to nearly indistinguishable bispectra of the equilateral type, but generate distinct patterns in the relative scaling of higher order moments. We illustrate these classes in a simple effective field theory framework where the flatness of the inflaton potential is protected by a softly broken shift symmetry. Since the distinctive difference between the two classes of interactions is the scaling of the moments, we investigate the implications for observables that depend on the series of moments. We obtain analytic expressions for the Minkowski functionals and the halo mass function for an arbitrary structure of moments, and use these to demonstrate how different classes of interactions might be distinguished observationally. Our analysis casts light on a number of theoretical issues, in particular we clarify the difference between the physics that keeps the distribution of fluctuations nearly Gaussian, and the physics that keeps the calculation under control.