Weighing neutrinos inf(R)gravity

Abstract

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 $\ensuremath{\sum}_{}^{}{m}_{\ensuremath{\nu}}$ and the effective number of neutrino species ${N}_{\mathrm{eff}}$. Then we constrain ${N}_{\mathrm{eff}}$ and $\ensuremath{\sum}_{}^{}{m}_{\ensuremath{\nu}}$ simultaneously. We find $\ensuremath{\sum}_{}^{}{m}_{\ensuremath{\nu}}<0.462\text{ }\text{ }\mathrm{eV}$ at a 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 ${N}_{\mathrm{eff}}={3.32}_{\ensuremath{-}0.51}^{+0.54}$ at a 95% confidence level for the same data set. When constraining ${N}_{\mathrm{eff}}$ and $\ensuremath{\sum}_{}^{}{m}_{\ensuremath{\nu}}$ simultaneously, we find ${N}_{\mathrm{eff}}={3.58}_{\ensuremath{-}0.69}^{+0.72}$ and $\ensuremath{\sum}_{}^{}{m}_{\ensuremath{\nu}}<0.860\text{ }\text{ }\mathrm{eV}$ at a 95% confidence level, respectively.