Study of primordial non-Gaussianity $f_{\mathrm{NL}}$ and $g_{\mathrm{NL}}$ with the cross-correlations between the scalar-induced gravitational waves and the cosmic microwave background

TL;DR

This paper investigates how cross-correlations between scalar-induced gravitational waves and the CMB can reveal primordial non-Gaussianity, offering a new method to probe the early universe's conditions.

Contribution

It provides a comprehensive analysis of the angular power spectra of these cross-correlations, highlighting their sensitivity to primordial non-Gaussianity and projecting future detection prospects.

Findings

Angular power spectra are highly sensitive to primordial non-Gaussianity.

Future gravitational-wave detectors can potentially measure primordial non-Gaussianity.

Cross-correlations offer a new avenue to study the early universe.

Abstract

The stochastic gravitational-wave background originating from cosmic sources contains vital information about the early universe. In this work, we comprehensively study the cross-correlations between the energy-density anisotropies in scalar-induced gravitational waves (SIGWs) and the temperature anisotropies and polarization in the cosmic microwave background (CMB). In our analysis of the angular power spectra for these cross-correlations, we consider all contributions of the local-type primordial non-Gaussianity $f_{\mathrm{NL}}$ and $g_{\mathrm{NL}}$ that can lead to large anisotropies. We show that the angular power spectra are highly sensitive to primordial non-Gaussianity. Furthermore, we project the sensitivity of future gravitational-wave detectors to detect such signals and, consequently, measure the primordial non-Gaussianity.