On Classification of Models of Large Local-Type Non-Gaussianity

TL;DR

This work develops a systematic classification of large local-type non-Gaussianity models using consistency relations among $f_{\rm NL}$, $\tau_{\rm NL}$, and $g_{\rm NL}$ within the $\delta N$ formalism. It separates models into single-source, multi-source, and constrained multi-source categories based on $\tau_{\rm NL}/(6 f_{\rm NL}/5)^2$ and analyzes explicit realizations (curvaton, modulated reheating, ungaussiton, etc.), including loop contributions. A key result is the universal local-type inequality $\tau_{\rm NL} \ge (6 f_{\rm NL}/5)^2$, which remains valid under subdominant loop corrections, and the diverse $f_{\rm NL}$–$g_{\rm NL}$ mappings across models that enable discrimination via trispectrum observations. The paper emphasizes that trispectrum measurements can distinctly reveal the generation mechanism of primordial fluctuations and guide future observational strategies.

Abstract

We classify models generating large local-type non-Gaussianity into some categories by using some "consistency relations" among the non-linearity parameters f_{NL}^{local}, τ_{NL}^{local} and g_{NL}^{local}, which characterize the size of bispectrum for the former and trispectrum for the later two. Then we discuss how one can discriminate models of large local-type non-Gaussianity with such relations. We first classify the models by using the ratio of τ_{NL}^{local}/(6f_{NL}^{local}/5)^2, which is unity for "single-source" models and deviates from unity for "multi-source" ones. We can make a further classification of models in each category by utilizing the relation between f_{NL}^{local} and g_{NL}^{local}. Our classification suggests that observations of trispectrum would be very helpful to distinguish models of large non-Gaussianity and may reveal the generation mechanism of primordial fluctuations.

Figures (4)

• Figure 1: $f_{\rm NL}$--$\tau_{\rm NL}$ diagram. The relation between $f_{\rm NL}$ and $\tau_{\rm NL}$ is shown for three categories: single-source, multi-source and constrained multi-source models. For multi-source and constrained multi-source models, the cases for some representative explicit models (mixed curvaton and inflaton, mixed modulated reheating and inflaton, and ungaussiton models) are plotted. All the three categories satisfy the inequality $\tau_{\rm NL} \gtrsim (6 f_{\rm NL} /5)^2$ as far as loop contributions are subdominant in the power spectrum. The region with $\tau_{\rm NL} < (6 f_{\rm NL}/5)^2$ is shaded with gray.
• Figure 2: $f_{\rm NL}$--$g_{\rm NL}$ diagram. The relation between $g_{\rm NL}$ and $f_{\rm NL}$ is plotted for models given in Table \ref{['tab:summary']}.
• Figure 3: Parameter regions where the curvaton fluctuations dominate over those from the modulated reheating in all orders (Region 1), and the fluctuations from modulated reheating dominate the curvaton ones, in the first and the third orders (Region 2), only in the second order (Region 3), and in all orders (Region 4). Note that here "all orders" just means "up to the third order" since we consider fluctuations only up to this order. We used $\alpha=\frac{1}{2}$ and $\beta=-1$ for illustrative purpose.
• Figure 4: Contours of $-C_{\rm mc}$ in the $f_{a1}$--$f_{b2}$ plane. Here we take $K=1$. Notice that, in the lower right and upper left region, $C_{\rm mc} \rightarrow - (10/3)$, which corresponds to the single curvaton case.