  The absolute neutrino mass scale is currently unknown, but can be constrained
from cosmology. The WiggleZ high redshift star-forming blue galaxy sample is
less sensitive to systematics from non-linear structure formation,
redshift-space distortions and galaxy bias than previous surveys. We obtain a
upper limit on the sum of neutrino masses of 0.60eV (95% confidence) for
WiggleZ+Wilkinson Microwave Anisotropy Probe. Combining with priors on the
Hubble Parameter and the baryon acoustic oscillation scale gives an upper limit
of 0.29eV, which is the strongest neutrino mass constraint derived from
spectroscopic galaxy redshift surveys.
