Induced gravitational waves from statistically anisotropic scalar perturbations. (arXiv:2205.07810v1 [astro-ph.CO])
<a href="http://arxiv.org/find/astro-ph/1/au:+Chen_C/0/1/0/all/0/1">Chao Chen</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Ota_A/0/1/0/all/0/1">Atsuhisa Ota</a>
The 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 the increasing source width. Our results
are helpful to test isotropy of primordial density perturbations at extremely
small scales through SIGWs.
The 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 the increasing source width. Our results
are helpful to test isotropy of primordial density perturbations at extremely
small scales through SIGWs.
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