The FLAMINGO Project: An assessment of the systematic errors in the predictions of models for galaxy cluster counts used to infer cosmological parameters

Galaxy cluster counts have historically been important for the measurement of cosmological parameters and upcoming surveys will greatly reduce the statistical errors. To exploit the potential of current and future cluster surveys, theoretical uncertainties on the predicted abundance must be smaller than the statistical errors. Models used to predict cluster counts typically combine a model for the dark matter only (DMO) halo mass function (HMF) with an observable - mass relation that is assumed to be a power-law with lognormal scatter. We use the FLAMINGO suite of cosmological hydrodynamical simulations to quantify the biases in the cluster counts and cosmological parameters resulting from the different ingredients of conventional models. For the observable mass proxy we focus on the Compton-Y parameter quantifying the thermal Sunyaev-Zel'dovich effect, which is expected to result in cluster samples that are relatively close to mass-selected samples. We construct three mock samples based on existing (Planck and SPT) and upcoming (Simons Observatory) surveys. We ignore measurement uncertainties and compare the biases in the counts and inferred cosmological parameters to each survey's Poisson errors. We find that widely used models for the DMO HMF differ significantly from each other and from the DMO version of FLAMINGO, leading to significant biases for all three surveys. For upcoming surveys, dramatic improvements are needed for all additional model ingredients, i.e. the functional forms of the fits to the observable-mass scaling relation and the associated scatter, the priors on the scaling relation and the prior on baryonic effects associated with feedback processes on the HMF.