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 analyze 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 is not sufficient for Euclid, Roman, Rubin or possible larger surveys. Future experiments will have to properly account for uncertainties in HMF parameters, and it will be necessary to improve the precision of HMF fits to avoid weakening constraints on cosmological parameters.

The simulation database of The Three Hundred Project has been used to pick synthetic clusters of galaxies with properties close to the observational targets of the NIKA2 camera Sunyaev–Zeldovich (SZ) Large Program. Cross–matching of cluster parameters such as mass and redshift of the cluster in the two databases has been implemented to generate the so–called twin samples for the Large Program. This SZ Large Program is observing a selection of galaxy clusters at intermediate and high redshift (0:5 < z < 0:9), covering one order of magnitude in mass. These are SZ–selected clusters from the Planck and Atacama Cosmology Telescope catalogs, wherein the selection is based on their integrated Compton parameter values, Y500: the value of the parameter within the characteristics radius R500. The Three Hundred hydrodynamical simulations provide us with hundreds of clusters satisfying these redshift, mass, and Y500 requirements. In addition to the standard post-processing analysis of the simulation, mock observational maps are available mimicking X–ray, optical, gravitational lensing, radio, and SZ observations of galaxy clusters. The primary goal of employing the twin samples is to compare different cluster mass proxies from synthetic X–ray, SZ effect and optical maps (via the velocity dispersion of member galaxies and lensing κ-maps) of the clusters. Eventually, scaling laws between different mass proxies and the cluster mass will be cross–correlated to reduce the scatter on the inferred mass and the mass bias will be related to various physical parameters.