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 $\mathrm{\Lambda }$CDM scenario ($\mathrm{\Lambda }$CDM $+ N_{\rm eff} + \sum m_{\nu} + c^2_{\rm eff} + c^2_{\rm vis} + \xi_{\nu}$) using the latest observational data from $\mathit{\text{Planck}}$ CMB (temperature power spectrum, low-polarisation and lensing reconstruction), baryon acoustic oscillations (BAOs) , the new recent local value of the Hubble constant from$\mathit{\text{Hubble}}\mathit{\text{Space}}\mathit{\text{Telescope}}$ ($\mathit{\text{HST}}$) and information of the abundance of galaxy clusters (GCs). We study the constraints on the CNB background using CMB + BAO + $\mathit{\text{HST}}$ data with and without the GC data. We find $\mathrm{\Delta }{N}_{\mathrm{e}\mathrm{f}\mathrm{f}}=0.614\pm 0.26$ 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 $\mathrm{\Lambda }$CDM $+N_{\mathrm{e}\mathrm{f}\mathrm{f}}+\sum m_{\nu }+{\xi }_{\nu }$ with the observational data. Within this scenario, we find $\mathrm{\Delta }{N}_{\mathrm{e}\mathrm{f}\mathrm{f}}=0.60\pm 0.28$ at 68 per cent confidence level. In both the scenarios, no mean deviations are found for the degeneracy parameter.