Anisotropic CMB distortions from non-Gaussian isocurvature perturbations

We calculate the CMB μ-distortion, ⟨μ⟩, and the angular power spectrum of its cross-correlation with the temperature anisotropy, ⟨μT⟩, in the presence of the non-Gaussian neutrino isocurvature density (NID) mode. While the pure Gaussian NID perturbations give merely subdominant contributions to ⟨μ⟩ and do not create ⟨μT⟩, we show large ⟨μT⟩ can be realized in case where, especially, the NID perturbations (x) are proportional to the square of a Gaussian field g(x), i.e. (x)∝ g²(x). Such Gaussian-squared perturbations contribute to not only the power spectrum, but also the bispectrum of CMB anisotropies. The constraints from the power spectrum is given by (k₀)∼_g²(k₀)≲10⁻¹⁰ at k₀=0.05 Mpc⁻¹. We also forecast constraints from the CMB temperature and E-mode polarisation bispectra, and show that _g(k₀)≲10⁻⁵ would be allowed from the Planck data. We find that ⟨μ⟩ and |l(l+1)C^μT_l| can respectively be as large as 10⁻⁹ and 10⁻¹⁴ with uncorrelated scale-invariant NID perturbations for _g(k₀)=10⁻⁵. When the spectrum of the Gaussian field is blue-tilted (with spectral index n_g≃1.5), ⟨μT⟩ can be enhanced by an order of magnitude.