Euclid preparation. XXIV. Calibration of the halo mass function in $\Lambda(\nu)$CDM cosmologies

TL;DR

This paper presents a highly precise calibration of the halo mass function for Euclid's galaxy cluster survey, accounting for simulation and methodological uncertainties to improve cosmological parameter estimation.

Contribution

It introduces a new Bayesian-calibrated analytic halo mass function model with sub-percent accuracy across various bcdm cosmologies, including massive neutrinos.

Findings

Calibration systematic uncertainty is sub-dominant to observational uncertainties.

Different halo finders can bias cosmological inferences if not properly accounted for.

The model achieves sub-percent accuracy across multiple bcdm variants.

Abstract

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 effects in the simulation. First, we test the convergence of HMF predictions from different N-body codes, by using initial conditions generated with different orders of Lagrangian Perturbation theory, and adopting different simulation box sizes and mass resolution. Then, we quantify the effect of using different halo-finder algorithms, and how the resulting differences 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 different spectral indexes, assuming both Einstein--de Sitter and standard $\Lambda$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 different variants of the $\Lambda$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 effect due to the halo finder, that could lead to biased cosmological inference.