Primordial Non-Gaussianity $f_{\mathrm{NL}}$ and Anisotropies in Scalar-Induced Gravitational Waves

TL;DR

This paper investigates how primordial non-Gaussianity influences anisotropies in scalar-induced gravitational waves, providing a comprehensive analysis of the angular power spectrum and its potential for future observational tests.

Contribution

It offers the first complete analysis of the angular power spectrum of scalar-induced gravitational wave anisotropies related to primordial non-Gaussianity, including frequency and multipole dependence.

Findings

Spectrum depends on initial inhomogeneities, Sachs-Wolfe effect, and crossing.

Frequency dependence and multipole scaling of $C_\ell( u)$ are characterized.

Potential for future space-borne detectors to measure $f_{ ext{NL}}$.

Abstract

Primordial non-Gaussianity encodes vital information of the physics of the early universe, particularly during the inflationary epoch. To explore the local-type primordial non-Gaussianity $f_{\mathrm{NL}}$, we study the anisotropies in gravitational wave background induced by the linear cosmological scalar perturbations during radiation domination in the early universe. We provide the first complete analysis to the angular power spectrum of such scalar-induced gravitational waves. The spectrum is expressed in terms of the initial inhomogeneities, the Sachs-Wolfe effect, and their crossing. It is anticipated to have frequency dependence and multipole dependence, i.e., $C_\ell(\nu)\propto [\ell(\ell+1)]^{-1}$ with $\nu$ being a frequency and $\ell$ referring to the $\ell$-th spherical harmonic multipole. In particular, the initial inhomogeneites in this background depend on gravitational-wave frequency. These properties are potentially useful for the component separation, foreground removal, and breaking degeneracies in model parameters, making the non-Gaussian parameter $f_{\mathrm{NL}}$ measurable. Further, theoretical expectations may be tested by space-borne gravitational-wave detectors in future.