Quadrupolar statistical anisotropy in initial conditions leaves cluster shapes unchanged but aligns the major axes of massive halos, more strongly for higher mass.
Statistically Anisotropic Tensor Modes from Inflation
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We consider the inflationary universe with a spectator scalar field coupled to a $U(1)$ gauge field and calculate curvature perturbation and gravitational waves (GWs). We find that the sourced GWs can be larger than the one from vacuum fluctuation and they are statistically anisotropic as well as linearly polarized. The GW power spectrum acquires higher multipole moments as $\mathcal{P}_h \propto (1-\cos^2\theta+\cos^4\theta-\cos^6\theta)$ irrespective of the model parameters.
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Shapes and orientations of massive halos in the statistically anisotropic universe
Quadrupolar statistical anisotropy in initial conditions leaves cluster shapes unchanged but aligns the major axes of massive halos, more strongly for higher mass.