Weighing Neutrinos with Galaxy Surveys

We show that galaxy redshift surveys sensitively probe the neutrino mass, with eV mass neutrinos suppressing power by a factor of 2. The Sloan Digital Sky Survey can potentially detect $N$ nearly degenerate massive neutrino species with mass $m_{\nu }\gtrsim 0.65({\Omega }_m{h}^2/0.1N{)}^{0.8}\mathrm{eV}$ at better than $2\sigma$ once microwave background experiments measure two other cosmological parameters. Significant overlap exists between this region and that implied by the Liquid Scintillator Neutrino Detector experiment, and even $m_{\nu }\sim 0.01–0.1\mathrm{eV}$, as implied by the atmospheric anomaly, can affect cosmological measurements.