Impact of the calibration of the Halo Mass Function on galaxy cluster
  number count cosmology
  The halo mass function (HMF) is a critical element in cosmological analyses
of galaxy cluster catalogs. We quantify the impact of uncertainties in HMF
parameters on cosmological constraints from cluster catalogs similar to those
from Planck, those expected from the Euclid, Roman and Rubin surveys, and from
a hypothetical larger future survey. We analyse simulated catalogs in each
case, gradually loosening priors on HMF parameters to evaluate the degradation
in cosmological constraints. While current uncertainties on HMF parameters do
not substantially impact Planck-like surveys, we find that they can
significantly degrade the cosmological constraints for a Euclid-like survey.
Consequently, the current precision on the HMF will not be sufficient for
Euclid (or Roman or Rubin) and possible larger surveys. Future experiments will
have to properly account for uncertainties in HMF parameters, and it will be
necessary to improve precision of HMF fits to avoid weakening constraints on
cosmological parameters.
