Induced gravitational waves from statistically anisotropic scalar perturbations

TL;DR

This paper studies how statistically anisotropic scalar perturbations during inflation can induce gravitational waves with anisotropic features, providing formulas and results to detect primordial anisotropy at small scales via gravitational wave observations.

Contribution

It introduces a framework to analyze anisotropic scalar perturbations' impact on induced gravitational waves, including explicit formulas for multipole moments and their dependence on source spectra.

Findings

SIGWs exhibit multipole anisotropies up to b64b4b4b4

Monopole spectrum has a high-b76b4b4b4 tail with a local minimum

Multipole moments broaden with increasing source width

Abstract

Scalar-induced gravitational waves (SIGWs) are attracting growing attention for probing extremely short-scale scalar perturbations via gravitational wave measurements. In this paper, we investigate the SIGWs from statistically anisotropic scalar perturbations, which are motivated in inflationary scenarios in the presence of, e.g., a vector field. While the ensemble average of the SIGW energy spectrum is isotropic for the standard statistically isotropic scalar perturbations, the statistical anisotropy in the source introduces the multipole moments of the differential SIGW energy spectrum. We consider quadrupole anisotropy in the scalar power spectrum and show that the SIGW spectrum has anisotropies up to $\ell=4$. We present generic formulas of the multipole moments and then apply them to the delta-function-like and log-normal source spectra. We find analytic expressions for the former case and show that the infrared scalings of the multipole moments are the same as the isotropic SIGWs. Interestingly, the monopole has an additional local minimum in the high-$k$ tail, a key feature to distinguish from the isotropic SIGWs. The latter log-normal case is analytic for the narrow-peak source, and we perform the numerical calculation for the broad peak. As one expects, the multipole moments become broader with increasing source width. Our results are helpful to test the isotropy of primordial density perturbations at extremely small scales through SIGWs.