The impact of the locally measured Hubble parameter on the mass of Sterile neutrino

Abstract: We present a precise analysis to test hypothetical models involving sterile neutrinos beyond the standard flat-$\Lambda$CDM cosmology with the CMB observations from the $Planck$ mission and BAO measurements. This analysis shows that adding the locally measured Hubble parameter $H_{0}$ = $73.00\pm1.75 $ km $\textrm s^{-1}$ Mp$\textrm c^{-1} $ to the data removes the need for the informative physical $m_{sterile}^{thermal}$ prior in CMB constraints of $ m_{\nu,sterile}^{eff}$. Under the constraints from the data containing the locally measured $H_{0}$ we obtain an upper limit $ m_{\nu,sterile}^{eff} < 0.306 $ eV scale mass for the massive sterile neutrino, and an upper limit $\Sigma m_{\nu} < 0.214$ eV scale mass for the three degenerate massive neutrino (95 per cent confidence level). We also obtain the value $\sigma_{8} $ = $0.81^{+0.05}_{-0.06} $ (95 per cent confidence level), which is in compatibility with the constraints from $Planck$ 2015 CMB data at the 1$\sigma$ level. We find that introducing parameter $ m_{\nu,sterile}^{eff}$ to the model of cosmology reduces the $\sigma_{8} $ value and moves it closer to the obtained value for this parameter from the KiDS-450 analysis. Our results show that the locally measured Hubble parameter can increase constraints on $\sigma_{8} $ values.