  We present the strongest current cosmological upper limit on the sum of
neutrino masses of < 0.18 (95% confidence). It is obtained by adding
observations of the large-scale matter power spectrum from the WiggleZ Dark
Energy Survey to observations of the cosmic microwave background data from the
Planck surveyor, and measurements of the baryon acoustic oscillation scale. The
limit is highly sensitive to the priors and assumptions about the neutrino
scenario. We explore scenarios with neutrino masses close to the upper limit
(degenerate masses), neutrino masses close to the lower limit where the
hierarchy plays a role, and addition of massive or massless sterile species.
