Statistical anisotropy in CMB spectral distortions

Abstract

Measurements of the cosmic microwave background (CMB) spectral $y$-distortion anisotropy offer a test for the statistical isotropy of the primordial density perturbations on $0.01\lesssim k\mathrm{Mpc}\lesssim 1$. We compute the 1-point ensemble averages of the $y$-distortion anisotropies which vanish for the statistically isotropic perturbations. For the quadrupole statistical anisotropy, we find $4\pi ⟨y_{2m}⟩=-6.8A_2\times 10^{-9}{Y}_{2m}(\mathbf{d})$ with the quadruple Legendre coefficient of the anisotropic powerspectrum $A_2$ and the $\ell =2$ spherical harmonics $Y_{2m}(\mathbf{d})$ for the preferred direction $\mathbf{d}$. Also, we discuss the cosmic variance of the $y$-distortion anisotropy in the statistically anisotropic Universe.

Comments: 5 pages, 4 figures, published version