Probing the properties of relic neutrinos using the cosmic microwave
  background, the Hubble Space Telescope and galaxy clusters
  We investigate the observational constraints on the cosmic neutrino
background (CNB) given by the extended $\Lambda$CDM scenario ($\Lambda$CDM $+
N_{\rm eff} + \sum m_{\nu} + c^2_{\rm eff} + c^2_{\rm vis} + \xi_{\nu}$) using
the latest observational data from \textit{Planck} CMB (temperature power
spectrum, low-polarisation and lensing reconstruction), baryon acoustic
oscillations (BAOs) , the new recent local value of the Hubble constant
from\textit{ Hubble Space Telescope} (\textit{HST}) and information of the
abundance of galaxy clusters (GCs). We study the constraints on the CNB
background using CMB + BAO + \textit{HST} data with and without the GC data. We
find $\Delta N_{\rm eff} = 0.614 \pm 0.26$ at 68 per cent confidence level when
the GC data are added in the analysis. We do not find significant deviation for
sound speed in the CNB rest frame. We also analyze the particular case
$\Lambda$CDM $+ N_{\rm eff} + \sum m_{\nu} + \xi_{\nu}$ with the observational
data. Within this scenario, we find $\Delta N_{\rm eff} = 0.60 \pm 0.28$ at 68
per cent confidence level. In both the scenarios, no mean deviations are found
for the degeneracy parameter.
