Effects of Completeness and Purity on Cluster Dark Energy Constraints
  The statistical properties of galaxy clusters can only be used for
cosmological purposes if observational effects related to cluster detection are
accurately characterized. These effects include the selection function
associated to cluster finder algorithms and survey strategy. The importance of
the selection becomes apparent when different cluster finders are applied to
the same galaxy catalog, producing different cluster samples. We consider
parametrized functional forms for the observable-mass relation, its scatter as
well as the completeness and purity of cluster samples, and study how prior
knowledge on these function parameters affects dark energy constraints derived
from cluster statistics. Under the assumption that completeness and purity
reach 50 % at masses around 10^{13.5} Msun/h, we find that self-calibration of
selection parameters in current and upcoming cluster surveys is possible, while
still allowing for competitive dark energy constraints. We consider a fiducial
survey with specifications similar to those of the Dark Energy Survey (DES)
with 5000 deg^2, maximum redshift of zmax ~ 1.0 and threshold observed mass
M_{th} ~ 10^{13.8} Msun/h, such that completeness and purity ~ 60 % - 80 % at
masses around M_{th}. Perfect knowledge of all selection parameters allows for
constraining a constant dark energy equation of state to sigma(w)=0.033.
Employing a joint fit including self-calibration of the effective selection
degrades constraints to sigma(w)=0.046. External calibrations at the level of 1
% in the parameters of the observable-mass relation and completeness/purity
functions are necessary to improve the joint constraints to sigma(w)=0.041. In
the lack of knowledge of selection parameters, future experiments probing
larger areas and greater depths suffer from stronger relative degradations on
dark energy constraints compared to current surveys.
