  We present cosmological upper limits on the sum of active neutrino masses
using large-scale power spectrum data from the WiggleZ Dark Energy Survey and
from the Sloan Digital Sky Survey - Data Release 7 (SDSS-DR7) sample of
Luminous Red Galaxies (LRG). Combining measurements on the Cosmic Microwave
Background temperature and polarisation anisotropies by the Planck satellite
together with WiggleZ power spectrum results in a neutrino mass bound of 0.37
eV at 95% C.L., while replacing WiggleZ by the SDSS-DR7 LRG power spectrum, the
95% C.L. bound on the sum of neutrino masses is 0.38 eV. Adding Baryon Acoustic
Oscillation (BAO) distance scale measurements, the neutrino mass upper limits
greatly improve, since BAO data break degeneracies in parameter space. Within a
$\Lambda$CDM model, we find an upper limit of 0.13 eV (0.14 eV) at 95% C.L.,
when using SDSS-DR7 LRG (WiggleZ) together with BAO and Planck. The addition of
BAO data makes the neutrino mass upper limit robust, showing only a weak
dependence on the power spectrum used. We also quantify the dependence of
neutrino mass limit reported here on the CMB lensing information. The tighter
upper limit (0.13 eV) obtained with SDSS-DR7 LRG is very close to that recently
obtained using Lyman-alpha clustering data, yet uses a completely different
probe and redshift range, further supporting the robustness of the constraint.
This constraint puts under some pressure the inverted mass hierarchy and
favours the normal hierarchy.
