Non-Gaussianity from Isocurvature Perturbations : Analysis of Trispectrum

TL;DR

This paper derives general expressions for the bispectrum and trispectrum of adiabatic and isocurvature perturbations, applying them to the QCD axion, and highlights the importance of future observations for understanding dark matter and baryon asymmetry.

Contribution

It provides new analytical formulas for non-Gaussianity measures in isocurvature perturbations and establishes a key consistency relation for the QCD axion scenario.

Findings

Derived formulas for bispectrum and trispectrum of perturbations.

Established a consistency relation between bispectrum and trispectrum coefficients.

Highlighted the significance of future trispectrum observations for cosmology.

Abstract

Non-Gaussianity may exist in the CDM isocurvature perturbation. We provide general expressions for the bispectrum and trispectrum of both adiabatic and isocurvature pertubations. We apply our result to the QCD axion case, and found a consistency relation between the coefficients of the bispectrum and trispectrum : tau_{NL}^(iso)~10^3 [f_{NL}^(iso)]^{4/3}, if the axion is dominantly produced by quantum fluctuation. Thus future observations of the trispectrum, as well as the bispectrum, will be important for understanding the origin of the CDM and baryon asymmetry.