Statistical anisotropy in CMB spectral distortions

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≲kMpc≲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 4π〈y2m〉=−6.8A2×10−9Y2m(d) with the quadruple Legendre coefficient of the anisotropic powerspectrum A2 and the ℓ=2 spherical harmonics Y2m(d) for the preferred direction d. Also, we discuss the cosmic variance of the y-distortion anisotropy in the statistically anisotropic Universe