  We perform a new study of future sensitivities of galaxy redshift surveys to
the free-streaming effect caused by neutrino masses, adding the information on
cosmological parameters from measurements of primary anisotropies of the cosmic
microwave background (CMB). Our reference cosmological scenario has nine
parameters and three different neutrino masses, with a hierarchy imposed by
oscillation experiments. Within the present decade, the combination of the
Sloan Digital Sky Survey (SDSS) and CMB data from the PLANCK experiment will
have a 2-sigma detection threshold on the total neutrino mass close to 0.2 eV.
This estimate is robust against the inclusion of extra free parameters in the
reference cosmological model. On a longer term, the next generation of
experiments may reach values of order sum m_nu = 0.1 eV at 2-sigma, or better
if a galaxy redshift survey significantly larger than SDSS is completed. We
also discuss how the small changes on the free-streaming scales in the normal
and inverted hierarchy schemes are translated into the expected errors from
future cosmological data.
