Galaxy cluster count cosmology with simulation-based inference

The abundance and mass distribution of galaxy clusters represents a sensitive probe of cosmological parameters, in particular through the sensitivity of the high-mass end of the halo mass function to Ωm and σ8. While galaxy cluster surveys have been used as cosmological probes for more than a decade, the accuracy of cluster-count experiments is still hampered by systematic uncertainties, such as the relation between survey observables and halo mass, the accuracy of the halo mass function, and the implementation of the survey-selection function. Here, we show that these uncertainties can be alleviated by forward-modeling the observed cluster population with simulation-based inference. We constructed a simulation pipeline that predicts the distribution of observables from cosmological parameters and scaling relations, and then we trained a neural network to learn the mapping between the input parameters and the measured distributions using neural density estimation. We focused on fiducial X-ray surveys with available flux, temperature, and redshift measurements, although the method can easily be adapted to any available observable quantity. We applied our method to mock observations extracted from the UNIT1i N-body simulation and demonstrate the accuracy of our approach. We then studied the impact of several important systematic uncertainties on the recovered cosmological parameters. We show that sample variance and the choice of the halo mass function are subdominant sources of systematic uncertainty. Conversely, the absolute mass scale is the leading source of systematic error and must be calibrated at the < 10% level to recover accurate values of Ωm and σ8. However, the quantity S8 = σ8(Ωm/0.3)0.3 appears to be much less sensitive to the accuracy of the mass calibration. We conclude that simulation-based inference is a promising avenue for future cosmological studies from galaxy cluster surveys such as eROSITA and Euclid as it makes it possible to consider all the available observables in a straightforward manner.