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.

In this talk, I compute the 1-point ensemble averages of the y-distortion harmonic coefficients.

They vanish for the statistically isotropic perturbations except for monopole, but I will show they don’t for the statistically anisotropic perturbations.