Neutrino anisotropies after Planck

Abstract

We present new constraints on the rest-frame sound speed, c_eff², and the viscosity parameter, c_vis², of the cosmic neutrino background from the recent measurements of the cosmic microwave background anisotropies provided by the Planck satellite. While broadly consistent with the expectations of c_eff²=c_vis²=1/3 in the standard scenario, the Planck data set hints at a higher value of the viscosity parameter, with c_vis²=0.60±0.18 at 68% C.L., and a lower value of the sound speed, with c_eff²=0.304±0.013 at 68% C.L. We find a correlation between the neutrino parameters and the lensing amplitude of the temperature power spectrum A_L. When the latter parameter is allowed to vary, we find a better consistency with the standard model with c_vis²=0.51±0.22, c_eff²=0.311±0.019, and A_L=1.08±0.18 at 68% C.L. This result indicates that the anomalous large value of A_L measured by Planck could be connected to nonstandard neutrino properties. Including additional data sets from baryon acoustic oscillation surveys and the Hubble Space Telescope constraint on the Hubble constant, we obtain c_vis²=0.40±0.19, c_eff²=0.319±0.019, and A_L=1.15±0.17 at 68% C.L.; including the lensing power spectrum, we obtain c_vis²=0.50±0.19, c_eff²=0.314±0.015, and A_L=1.025±0.076 at 68% C.L. Finally, we investigate further degeneracies between the clustering parameters and other cosmological parameters.