Weighing Neutrinos in $f(R)$ gravity

We constrain the neutrino properties in $f(R)$ gravity using the latest observations from cosmic microwave background(CMB) and baryon acoustic oscillation(BAO) measurements. We first constrain separately the total mass of neutrinos $\sum m_{\nu }$ and the effective number of neutrino species $N_{\rm eff}$\mathrm{.}Thenweconstrain$N_{\rm eff}$and$\sum m_\nu$simultaneously\mathrm{.}Wefind$\sum m_\nu<0.462 {\rm eV}$ata$95%$ confidence level for the combination of Planck CMB data, WMAP CMB polarization data, BAO data and high-$l$ data from the Atacama Cosmology Telescope and the South Pole Telescope. We also find $N_{\mathrm{e}\mathrm{f}\mathrm{f}}=3.32_{-0.51}^{+0.54}$ at a $95\mathrm{\%}$ confidence level for the same data set. When constraining $N_{\mathrm{e}\mathrm{f}\mathrm{f}}$ and $\sum m_{\nu }$ simultaneously, we find $N_{\mathrm{e}\mathrm{f}\mathrm{f}}=3.58_{-0.69}^{+0.72}$ and $\sum m_{\nu }<0.860\mathrm{e}\mathrm{V}$ at a $95\mathrm{\%}$ confidence level, respectively.