Euclid preparation. XXIV. Calibration of the halo mass function in Lambda_nu-CDM cosmologies

Euclid’s photometric galaxy cluster survey has the potential to be a very competitive cosmological probe. The main cosmological probe with observations of clusters is their number count, within which the halo mass function (HMF) is a key theoretical quantity. We present a new calibration of the analytic HMF, at the level of accuracy and precision required for the uncertainty in this quantity to be subdominant with respect to other sources of uncertainty in recovering cosmological parameters from Euclid cluster counts. Our model is calibrated against a suite of N-body simulations using a Bayesian approach taking into account systematic errors arising from numerical e ects in the simulation. First, we test the convergence of HMF predictions from di erent N-body codes, by using initial conditions generated with di erent orders of Lagrangian Perturbation theory, and adopting di erent simulation box sizes and mass resolution. Then, we quantify the e ect of using di erent halo finder algorithms, and how the resulting di erences propagate to the cosmological constraints. In order to trace the violation of universality in the HMF, we also analyse simulations based on initial conditions characterised by scale-free power spectra with di erent spectral indexes, assuming both Einstein–de Sitter and standard  CDM expansion histories. Based on these results, we construct a fitting function for the HMF that we demonstrate to be sub-percent accurate in reproducing results from 9 di erent variants of the  CDM model including massive neutrinos cosmologies. The calibration systematic uncertainty is largely sub-dominant with respect to the expected precision of future mass–observation relations; with the only notable exception of the e ect due to the halo finder, that could lead to biased cosmological inference.