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 ${m}_{\ensuremath{\nu}}\ensuremath{\gtrsim}0.65({\ensuremath{\Omega}}_{m}{h}^{2}/0.1N{)}^{0.8}\phantom{\rule{0ex}{0ex}}\mathrm{eV}$ at better than $2\ensuremath{\sigma}$ 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 ${m}_{\ensuremath{\nu}}\ensuremath{\sim}0.01\char21{}0.1\mathrm{eV}$, as implied by the atmospheric anomaly, can affect cosmological measurements.