Weighing neutrinos with galaxy cluster surveys

Large future galaxy cluster surveys, combined with cosmic microwave background observations, can achieve a high sensitivity to the masses of cosmologically important neutrinos. We show that a weak lensing selected sample of >= 100 000 clusters could tighten the current upper bound on the sum of masses of neutrino species by an order of magnitude, to a level of 0.03 eV. Since this statistical sensitivity is below the best existing lower limit on the mass of at least one neutrino species, a future detection is likely, provided that systematic errors can be controlled to a similar level.