Constraints on μ-distortion fluctuations and primordial non-Gaussianity from Planck data

We use the Planck HFI channel maps to make an all sky map of μ-distortion fluctuations. Our μ-type distortion map is dominated by the y-type distortion contamination from the hot gas in the low redshift Universe and we can thus only place upper limits on the μ-type distortion fluctuations. For the amplitude of μ-type distortions on 10' scales we get the limit on root mean square (rms) value μ_rms^10'< 6.4× 10⁻⁶, a limit 14 times stronger than the COBE-FIRAS (95% confidence) limit on the mean of ( μ )<90× 10⁻⁶. Using our maps we also place strong upper limits on the auto angular power spectrum of μ, C_ℓ^μμ and the cross angular power spectrum of μ with the CMB temperature anisotropies, C_ℓ^μ T. The strongest observational limits are on the largest scales, ℓ(ℓ+1)/(2π)C_ℓ^μμ|_ℓ=2−26<(2.3± 1.0)× 10⁻¹² and ℓ(ℓ+1)/(2π)C_ℓ^μ T|_ℓ=2−26<(2.6± 2.6)× 10⁻¹² K. Our observational limits can be used to constrain new physics which can create spatially varying energy release in the early Universe between redshifts 5× 10^4∼< z∼< 2× 10⁶. We specifically apply our observational results to constrain the primordial non-Gaussianity of the local type, when the source of μ-distortion is Silk damping, for very squeezed configurations with the wavenumber for the short wavelength mode 46 ∼< k_S ∼< 10⁴ Mpc⁻¹ and for the long wavelength mode k_L≈ 10⁻³ Mpc⁻¹. Our limits on the primordial non-Gaussianity parameters are f_NL<10⁵, τ_NL<1.4× 10¹¹ for k_S/k_L≈ 5× 10⁴− 10⁷. We also give a new derivation of the evolution of the μ-distortion fluctuations through the y-distortion era and the recombination epoch until today resulting in very simple expressions for the cross and auto power spectra in the squeezed limit. We also introduce mixing of Bose-Einstein spectra due to Silk damping and y^BE-type distortions. The μ-type distortion map and masks are now publicly available