Constraints on $\mu$-distortion fluctuations and primordial non-Gaussianity from Planck data

Abstract

We use the Planck HFI channel maps to make an all sky map of $\mu$-distortion fluctuations. Our $\mu$-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 $\mu$-type distortion fluctuations. For the amplitude of $\mu$-type distortions on $10^{\prime }$ scales we get the limit on root mean square (rms) value ${\mu }_{rms}^{10^{\prime }}<6.4\times 10^{-6}$, a limit 14 times stronger than the COBE-FIRAS ($95\%$ confidence) limit on the mean of $<\mu ><90\times 10^{-6}$. Using our maps we also place strong upper limits on the auto angular power spectrum of $\mu$, $C_{\ell }^{\mu \mu }$ and the cross angular power spectrum of $\mu$ with the CMB temperature anisotropies, $C_{\ell }^{\mu T}$. The strongest observational limits are on the largest scales, $\ell (\ell +1)/(2\pi )C_{\ell }^{\mu \mu }{|}_{\ell =2-26}<(2.3\pm 1.0)\times 10^{-12}$ and $\ell (\ell +1)/(2\pi )C_{\ell }^{\mu T}{|}_{\ell =2-26}<(2.6\pm 2.6)\times 10^{-12}K$. Our observational limits can be used to constrain new physics which can create spatially varying energy release in the early Universe between redshifts $5\times 10^4\lesssim z\lesssim 2\times 10^6$. We specifically apply our observational results to constrain the primordial non-Gaussianity of the local type, when the source of $\mu$-distortion is Silk damping, for very squeezed configurations with the wavenumber for the short wavelength mode $46\lesssim k_S\lesssim 10^{4}Mp{c}^{-1}$ and for the long wavelength mode $k_L\approx 10^{-3}Mp{c}^{-1}$. Our limits on the primordial non-Gaussianity parameters are $f_{NL}<10^5,{\tau }_{NL}<1.4\times 10^{11}$ for $k_S/k_L\approx 5\times 10^4-10^7$. We give a new derivation of the evolution of the $\mu$-distortion fluctuations. We also introduce mixing of Bose-Einstein spectra and $y^{BE}$-type distortions.

The μ-distortion map and masks are publicly available at http://www.mpa-garching.mpg.de/~khatri/muresults/

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