Neutrino masses and cosmological parameters from a Euclid-like survey:
  Markov Chain Monte Carlo forecasts including theoretical errors
  We present forecasts for the accuracy of determining the parameters of a
minimal cosmological model and the total neutrino mass based on combined mock
data for a future Euclid-like galaxy survey and Planck. We consider two
different galaxy surveys: a spectroscopic redshift survey and a cosmic shear
survey. We make use of the Monte Carlo Markov Chains (MCMC) technique and
assume two sets of theoretical errors. The first error is meant to account for
uncertainties in the modelling of the effect of neutrinos on the non-linear
galaxy power spectrum and we assume this error to be fully correlated in
Fourier space. The second error is meant to parametrize the overall residual
uncertainties in modelling the non-linear galaxy power spectrum at small
scales, and is conservatively assumed to be uncorrelated and to increase with
the ratio of a given scale to the scale of non-linearity. It hence increases
with wavenumber and decreases with redshift. With these two assumptions for the
errors and assuming further conservatively that the uncorrelated error rises
above 2% at k = 0.4 h/Mpc and z = 0.5, we find that a future Euclid-like cosmic
shear/galaxy survey achieves a 1-sigma error on Mnu close to 32 meV/25 meV,
sufficient for detecting the total neutrino mass with good significance. If the
residual uncorrelated errors indeed rises rapidly towards smaller scales in the
non-linear regime as we have assumed here then the data on non-linear scales
does not increase the sensitivity to the total neutrino mass. Assuming instead
a ten times smaller theoretical error with the same scale dependence, the error
on the total neutrino mass decreases moderately from sigma(Mnu) = 18 meV to 14
meV when mildly non-linear scales with 0.1 h/Mpc < k < 0.6 h/Mpc are included
in the analysis of the galaxy survey data.
