Cosmology with galaxy cluster properties using machine learning

Galaxy clusters are the largest gravitating structures in the universe, and their mass assembly is sensitive to the underlying cosmology. Their mass function, baryon fraction, and mass distribution have been used to infer cosmological parameters despite the presence of systematics. However, the complexity of the scaling relations among galaxy cluster properties has never been fully exploited, limiting their potential as a cosmological probe. We propose the first machine learning (ML) method using galaxy cluster properties from hydrodynamical simulations in different cosmologies to predict cosmological parameters combining a series of canonical cluster observables, such as gas mass, gas bolometric luminosity, gas temperature, stellar mass, cluster radius, total mass, and velocity dispersion at different redshifts. The ML model was trained on mock ``measurements'' of these observable quantities from Magneticum multi-cosmology simulations to derive unbiased constraints on a set of cosmological parameters. These include the mass density parameter, $ the power spectrum normalization, $ the baryonic density parameter, $ and the reduced Hubble constant, $h_0$. We tested the ML model on catalogs of a few hundred clusters taken, in turn, from each simulation and found that the ML model can correctly predict the cosmology from where they have been picked. The cumulative accuracy depends on the cosmology, ranging from 21 to 75. We demonstrate that this is sufficient to derive unbiased constraints on the main cosmological parameters with errors on the order of for $ for $ for $ and $ $ for $h_0$. This proof-of-concept analysis, though based on a limited variety of multi-cosmology simulations, shows that ML can efficiently map the correlations in the multidimensional space of the observed quantities to the cosmological parameter space and narrow down the probability that a given sample belongs to a given cosmological parameter combination. More large-volume, mid-resolution, multi-cosmology hydro-simulations need to be produced to expand the applicability to a wider cosmological parameter range. However, this first test is exceptionally promising, as it shows that these ML tools can be applied to cluster samples from multiwavelength observations from surveys such as Rubin/LSST, CSST, Euclid, and Roman in optical and near-infrared bands, and eROSITA in X-rays, to the constrain cosmology and effect of baryonic feedback.