The Trispectrum in the Multi-brid Inflation

TL;DR

This work analyzes the trispectrum of local-type non-Gaussianity in a two-brid multi-field inflation model using the $\delta N$ formalism. It derives explicit expressions for $f_{NL}$, $τ_{NL}$, and $g_{NL}$ in terms of the model parameters, showing that $τ_{NL}$ is positive and closely tied to $f_{NL}$ by $τ_{NL}=\frac{36}{25}\frac{1}{\tilde c^2} f_{NL}^2$, while $g_{NL}$ can have either sign and a wide range of magnitudes. In the symmetric case $g_1=g_2$, $g_{NL}=2 f_{NL}^2$ and $τ_{NL}\gtrsim \frac{36}{25} f_{NL}^2$ for small tensor-to-scalar ratio, whereas in the asymmetric case $g_1\neq g_2$ large negative $g_{NL}$ is possible with sizable $f_{NL}$. The results emphasize that the trispectrum can be as informative as the bispectrum for discriminating multi-brid inflation from curvaton scenarios and motivate further observational focus on $τ_{NL}$ and $g_{NL}$.

Abstract

The trispectrum is at least as important as the bispectrum and its size can be characterized by two parameters $τ_{NL}$ and $g_{NL}$. In this short paper, we focus on the Multi-brid inflation, in particular the two-brid inflation model in arXiv.0805.0974, and find that $τ_{NL}$ is always positive and roughly equals to $({6\over 5}f_{NL})^2$ for the low scale inflation, but $g_{NL}$ can be negative or positive and its order of magnitude can be the same as that of $τ_{NL}$ or even larger