Detecting the cosmological neutrino background in the CMB

TL;DR

The paper tests whether the cosmological neutrino background imprints on the CMB can be interpreted as free streaming particles or alternatively as a relativistic fluid. By solving the neutrino Boltzmann hierarchy and comparing against models where neutrinos act as a relativistic perfect fluid or a viscous fluid, using Planck-2013 data (withWMAP polarization) and full MCMC analyses, the authors show that free streaming is decisively preferred, with $\Delta\chi^2$ of about 21–20 for fluid models. Allowing additional fluid parameters like $c_{ m eff}^2$ and $c_{ m vis}^2$ yields only marginal improvements, not justifying the more complex models per Occam’s razor, and fixed-$N_{ m eff}$ analyses reinforce the robustness of the result. The conclusion strengthens indirect evidence for the cosmological neutrino background and demonstrates the CMB’s sensitivity to neutrino clustering properties beyond mere energy density, consistent with standard three neutrino species.

Abstract

Three relativistic particles in addition to the photon are detected in the cosmic microwave background (CMB). In the standard model of cosmology, these are interpreted as the three neutrino species. However, at the time of CMB-decoupling, neutrinos are not only relativistic but they are also freestreaming. Here, we investigate, whether the CMB is sensitive to this defining feature of neutrinos, or whether the CMB-data allow to replace neutrinos with a relativistic fluid. We show that free streaming particles are preferred over a relativistic perfect fluid with $Δχ^2\simeq 21$. We also study the possibility to replace the neutrinos by a viscous fluid and find that a relativistic viscous fluid with either the standard values $c_{\rm eff}^2=c_{\rm vis}^2=1/3$ or best fit values for $c_{\rm eff}^2$ and $c_{\rm vis}^2$ has $Δχ^2=20$ and thus cannot provide a good fit to present CMB data either.

Figures (7)

• Figure 1: The temperature anisotropy spectra at fixed cosmological parameters for different values of the cutoff in the neutrino hierarchy, $\ell_{\max}^\nu=1,2,3,6,8,17$. For $\ell_{\max}^\nu>2$ the result changes very little. In the bottom panel, the difference between $C_\ell$ for the viscous neutrino fluid ($\ell_{\max}^\nu=2$) and free streaming neutrinos, is compared to cosmic variance, which roughly corresponds to the Planck error out to $\ell\simeq 2000$. For low $\ell$ cosmic variance does not allow to discriminate between the viscous fluid model and free streaming neutrinos, but for high $\ell$ the difference between these two models is up to three times larger than cosmic variance $\sigma_{cv} = C^{\rm free}_\ell \cdot \sqrt{2/(2\ell +1)f_{sky}}$. (Note that here $\ell_{\max}^\nu$ denotes the maximal neutrino multipole while $\ell$ refers to the CMB multipoles.)
• Figure 2: The improvement of the fit, $\Delta \chi^2 = \chi^2(\ell_{\max}^\nu) - \chi^2 (\ell_{\max}^\nu = 17)$, as a function of the maximal considered neutrino multipole $\ell_{\max}^\nu$ in the Liouville equations for the neutrinos. free streaming neutrinos correspond to $\Delta \chi^2 = 0$.
• Figure 3: The temperature anisotropy spectra for best fit parameters modeling neutrinos as a perfect fluid (blue), a relativistic viscous fluid (red) and standard free streaming neutrinos (black) are shown. The difference of the best fit spectra is not visible by eye. However, from the plot at the bottom which shows the difference in units of the cosmic variance error it is clear, that the Planck experiment can distinguish the spectra.
• Figure 4: The best fit parameters for neutrinos modeled as a perfect fluid (blue), as a relativistic viscous fluid (orange), as a viscous fluid with arbitrary sound speed $c_{\rm eff}^2$ and viscosity $c_{\rm vis}^2$ (green), and as standard free streaming neutrinos (black) are shown. We also show free streaming neutrinos with different $\ell^\nu_{\max}$ as indicated in the legend in light blue to grey shades. The best fit values of several parameters for the perfect fluid and the free streaming model differ significantly. The best fit values of most parameters for the viscous fluid and the free streaming model are similar, they all agree within $1.5\sigma$ apart from $n_s$ which for the relativistic viscous fluid model differs by more than $2\sigma$. Truncating the Boltzmann hierarchy for the neutrinos at other maximally allowed $\ell \geq 3$ (indicated in different shades of blue) leads to parameter constraints that are indistinguishable from the standard Planck fit, consistent with Fig. \ref{['f:comp']}. Allowing also $N_{\rm eff}$ does not change these results, as can be seen in Fig. \ref{['Neff']} in the appendix.
• Figure 5: The best fit parameters for neutrinos modeled as a viscous fluid with variable $c_{\rm eff}^2$ and $c_{\rm vis}^2$ and $\ell^\nu_{max = 2}$ (blue), for neutrinos modeled as a viscous free streaming fluid with $\ell^\nu_{max} = 17$(orange), and for standard free streaming neutrinos (green) are shown. The best fit values of most parameters for the two different viscosity models differ by about one standard deviation.