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 $\gtrsim 100000$ 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.

Figure 1

The total mass and three mass eigenvalues of neutrinos as a function of the unknown smallest mass $m_1$ [34]. A normal hierarchy is assumed. In our analysis, we consider the scenario of three families of neutrinos with one massive and two massless. The upper dotted line shows the current most robust $1\sigma$ limit [4]. The lower dotted lines show our predicted $1\sigma$ constraints, for two different sets of weak lensing selection efficiency and completeness, from combining all three cluster surveys and Planck.