Study of primordial non-Gaussianity fNL and gNL with the cross-correlations between the scalar-induced gravitational waves and the cosmic microwave background

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 and the temperature anisotropies and polarization in the cosmic microwave background. In our analysis of the angular power spectra for these cross-correlations, we consider all contributions of the local-type primordial non-Gaussianity fNL f NL and gNL g 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.