We perform a detailed forecast on how well a Euclid-like photometric galaxy
and cosmic shear survey will be able to constrain the absolute neutrino mass
scale. Adopting conservative assumptions about the survey specifications and
assuming complete ignorance of the galaxy bias, we estimate that the minimum
mass sum of sum m_nu ~ 0.06 eV in the normal hierarchy can be detected at 1.5
sigma to 2.5 sigma significance, depending on the model complexity, using a
combination of galaxy and cosmic shear power spectrum measurements in
conjunction with CMB temperature and polarisation observations from Planck.
With better knowledge of the galaxy bias, the significance of the detection
could potentially reach 5.4 sigma. Interestingly, neither Planck+shear nor
Planck+galaxy alone can achieve this level of sensitivity; it is the combined
effect of galaxy and cosmic shear power spectrum measurements that breaks the
persistent degeneracies between the neutrino mass, the physical matter density,
and the Hubble parameter. Notwithstanding this remarkable sensitivity to sum
m_nu, Euclid-like shear and galaxy data will not be sensitive to the exact mass
spectrum of the neutrino sector; no significant bias (< 1 sigma) in the
parameter estimation is induced by fitting inaccurate models of the neutrino
mass splittings to the mock data, nor does the goodness-of-fit of these models
suffer any significant degradation relative to the true one (Delta chi_eff ^2<
1).Comment: v1: 29 pages, 10 figures. v2: 33 pages, 12 figures; added sections on
shape evolution and constraints in more complex models, accepted for
publication in JCA
