Feeding your Inflaton: Non-Gaussian Signatures of Interaction Structure

TL;DR

This work analyzes how two distinct inflationary NG mechanisms—the inflaton's self-interactions and feeder-type couplings to other sectors—produce nearly identical equilateral bispectra but fundamentally different higher-moment structures. By formulating a shift-symmetric EFT for the inflaton and defining dimensionless moments $\mathcal{M}_n$, the authors show that self-interactions yield hierarchical scaling $\mathcal{M}_n \propto (\mathcal{I}^2 2\pi^2 \mathcal{P}_{\zeta})^{(n-2)/2}$, while feeder mechanisms generate non-hierarchical patterns with markedly different higher-order cumulants. They compute analytic expressions for the Minkowski functionals and halo mass function under arbitrary moment structures, and discuss observational avenues—especially involving rare objects and morphology—that can distinguish the two classes. The results emphasize that NG constraints should go beyond the bispectrum, as the pattern of higher moments encodes critical information about the underlying microphysics of inflation and its couplings. This provides a framework for interpreting future measurements of higher-order statistics in the CMB and LSS to identify the correct inflationary scenario.

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.

Figures (3)

• Figure 1: A comparison of the scaling behaviors. All cases have been normalized to give the same value of $\mathcal{M}_3$. The purple diamonds show the standard hierarchical scaling, generated by derivative self-interactions and the local ansatz, for example. For a fixed amplitude of the bispectrum, scenarios of this type are the least non-Gaussian of the scalings discussed here. The brown circles show a hierarchical scaling with an extra parametric dependence in the individual moments, as occurs in resonant non-Gaussianity or the mixed inflaton/curvaton scenario. This last case should also mimic some of the difference that might come from having very different $A_n$ factors. The blue stars show the feeder field scaling given for example from the inverse decay, particle production and "un-Gaussiton" scenarios.
• Figure 2: The ratio of the non-Gaussian to Gaussian mass function for redshifts $z=0$ and $z=0.5$. Each panel shows a set of lower curves that assume equilateral non-Gaussianity corresponding to $f_{NL}=100$ and upper curves corresponding to $f_{NL}=250$. In each set of curves, the black solid lines shows the result for the pdf truncated at $\mathcal{M}_{3,R}$ while the blue dashed and purple dotted lines show the second order result for the hierarchical and feeder field scalings respectively. Notice that the range of masses where the fourth moment is a significant correction is model dependent. Finally, the red dot-dashed lines shows the next order ($\mathcal{M}_{5,R}$) correction for the feeder field scenario.
• Figure 3: A comparison of the predictions from the second order Edgeworth and Log-Edgeworth mass functions. The ratio of the non-Gaussian to Gaussian mass functions of each type is plotted versus mass for redshifts $z=0$ and $z=0.5$. Each panel shows the hierarchical (lower curves) and feeder field (upper curves) scaling assuming an equilateral type bispectrum with amplitude corresponding to $f_{NL}^{equil}=250$. The solid black lines show the second order Edgeworth result for hierarchical scaling. The dashed red lines are the Log-Edgeworth expansions for the hierarchical case and are indistinguishable from the Edgeworth for the parameters plotted here. The dashed black lines show the Edgeworth expansion for the feeder field scaling, and the dot-dashed blue lines show the Log-Edgeworth. Interestingly, the second-order Log-Edgeworth for the feeder field corresponds very nearly with the fourth order Edgeworth expansion (see previous figure).