Cosmology in 2D: the concentration-mass relation for galaxy clusters
  The aim of this work is to perform a systematic study of the measures of the
mass and concentration estimated by fitting the convergence profile of a large
sample of mock galaxy cluster size lenses, created with the publicly available
code MOKA. We found that the main contribution to the bias in mass and in
concentration is due to the halo triaxiality and second to the presence of
substructures within the host halo virial radius. We show that knowing the
cluster elongation along the line of sight helps in correcting the mass bias,
but still keeps a small negative bias for the concentration. If these mass and
concentration biases will characterize the galaxy cluster sample of a wide
field survey it will be difficult to well recover within one sigma the
cosmological parameters that mainly influence the c - M relation, using as
reference a 3D c - M relation measured in cosmological N-body simulation. In
this work we propose how to correct the c - M relation for projection effects
and for adiabatic contraction and suggest to use these as reference for real
observed data. Correcting mass and concentration estimates, as we propose,
gives a measurement of the cosmological parameter within 1 - {\sigma}
confidence contours.
