Detecting the cosmological neutrino background in the CMB

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 $\Delta\chi^2\simeq 21$. 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 $\Delta\chi^2=20$ and thus cannot provide a good fit to present CMB data either.