Neutrino Anisotropies after Planck

TL;DR

This paper tests the clustering properties of the Cosmic Neutrino Background by constraining the rest-frame sound speed $c_{\rm eff}^2$ and the viscosity parameter $c_{\rm vis}^2$ within a Generalized Dark Matter framework using Planck CMB data. The authors explore degeneracies with the CMB lensing amplitude $A_L$ by analyzing Planck data alone and in combination with BAO/HST and Planck lensing, employing CosmoMC to sample extended cosmological parameter spaces. They find that Planck data alone prefer non-standard values for the neutrino clustering parameters, but allowing $A_L$ to vary and including additional datasets moves the results toward the standard $c_{\rm eff}^2=c_{\rm vis}^2=1/3$ with $A_L$ near unity; the strongest full-dataset result shows $c_{\rm eff}^2\approx0.314$, $c_{\rm vis}^2\approx0.50$, and $A_L\approx1.025$, consistent with standard physics within uncertainties. The work highlights a nontrivial degeneracy between neutrino perturbation properties and lensing in the Planck data and demonstrates that incorporating lensing and external measurements can reconcile potential anomalies with the standard cosmological model.

Abstract

We present new constraints on the rest-frame sound speed, c_{eff}^2, and the viscosity parameter, c_{vis}^2, 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_{eff}^2=c_{vis}^2=1/3 in the standard scenario, the Planck dataset hints at a higher value of the viscosity parameter, with c_{vis}^2=0.60+/-0.18 at 68% c.l., and a lower value of the sound speed, with c_{eff}^2=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_{vis}^2=0.51+/-0.22, c_{eff}^2=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 non-standard neutrino properties. Including additional datasets from Baryon Acoustic Oscillation surveys and the Hubble Space Telescope constraint on the Hubble constant, we obtain c_{vis}^2=0.40+/-0.19, c_{eff}^2=0.319+/-0.019, and A_{L}=1.15+/-0.17 at 68% c.l.; including the lensing power spectrum, we obtain c_{vis}^2=0.50+/-0.19, c_{eff}^2=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.

Figures (8)

• Figure 1: One-dimensional posterior probabilities of the parameter $c_{\rm eff}^2$ for the indicated models for $PlanckWP$ (upper left), $PlanckEX$ (upper right) and $PlanckL$ (bottom) datasets. The vertical dashed line indicates the expected value in the standard model. Note the different range in the $x$ axes for the $PlanckL$ dataset.
• Figure 2: One-dimensional posterior probabilities of the parameter $c_{\rm vis}^2$ for the indicated models for $PlanckWP$ (upper left), $PlanckEX$ (upper right) and $PlanckL$ (bottom) datasets. The vertical dashed line indicates the expected value in the standard model.
• Figure 3: One-dimensional posterior probabilities of the parameter $A_{\rm L}$ for the indicated models for $PlanckWP$ (upper left), $PlanckEX$ (upper right) and $PlanckL$ (bottom) datasets. The vertical dashed line indicates the expected value in the standard model. Note the different range in the $x$ axes for the $PlanckL$ dataset.
• Figure 4: Degeneracy between the clustering parameters $c_{\rm eff}^2$ (left) and $c_{\rm vis}^2$ and the scalar spectral index $n_S$ for the $PlanckWP$ dataset and the indicated models.
• Figure 5: Degeneracy between the clustering parameters $c_{\rm eff}^2$ (left) and $c_{\rm vis}^2$ and the scalar amplitude $A_S$ for the $PlanckWP$ dataset and the indicated models.