  Solar, atmospheric, and reactor neutrino experiments have confirmed neutrino
oscillations, implying that neutrinos have non-zero mass, but without pinning
down their absolute masses. While it is established that the effect of
neutrinos on the evolution of cosmic structure is small, the upper limits
derived from large-scale structure data could help significantly to constrain
the absolute scale of the neutrino masses. In a recent paper the 2dF Galaxy
Redshift Survey (2dFGRS) team provided an upper limit m_nu,tot < 2.2 eV, i.e.
approximately 0.7 eV for each of the three neutrino flavours, or phrased in
terms of their contributioin to the matter density, Omega_nu/Omega_m < 0.16.
Here we discuss this analysis in greater detail, considering issues of assumed
'priors' like the matter density Omega_m and the bias of the galaxy
distribution with respect the dark matter distribution. As the suppression of
the power spectrum depends on the ratio Omega_nu/Omega_m, we find that the
out-of- fashion Mixed Dark Matter Model, with Omega_nu=0.2, Omega_m=1 and no
cosmological constant, fits the 2dFGRS power spectrum and the CMB data
reasonably well, but only for a Hubble constant H_0<50 km/s/Mpc. As a
consequence, excluding low values of the Hubble constant, e.g. with the HST Key
Project is important in order to get a strong constraint on the neutrino
masses. We also comment on the improved limit by the WMAP team, and point out
that the main neutrino signature comes from the 2dFGRS and the Lyman alpha
forest.
