Constraints on the Neutrino Mass from SZ Surveys
  Statistical measures of galaxy clusters are sensitive to neutrino masses in
the sub-eV range. We explore the possibility of using cluster number counts
from the ongoing PLANCK/SZ and future cosmic-variance-limited surveys to
constrain neutrino masses from CMB data alone. The precision with which the
total neutrino mass can be determined from SZ number counts is limited mostly
by uncertainties in the cluster mass function and intracluster gas evolution;
these are explicitly accounted for in our analysis. We find that projected
results from the PLANCK/SZ survey can be used to determine the total neutrino
mass with a (1\sigma) uncertainty of 0.06 eV, assuming it is in the range
0.1-0.3 eV, and the survey detection limit is set at the 5\sigma significance
level. Our results constitute a significant improvement on the limits expected
from PLANCK/CMB lensing measurements, 0.15 eV. Based on expected results from
future cosmic-variance-limited (CVL) SZ survey we predict a 1\sigma uncertainty
of 0.04 eV, a level comparable to that expected when CMB lensing extraction is
carried out with the same experiment. A few percent uncertainty in the mass
function parameters could result in up to a factor \sim 2-3 degradation of our
PLANCK and CVL forecasts. Our analysis shows that cluster number counts provide
a viable complementary cosmological probe to CMB lensing constraints on the
total neutrino mass.
