Cosmology with galaxy clusters using machine learning. Application to eROSITA Data

TL;DR

The first Cosmological Parameter inferences from eROSITA X-ray observations of galaxy clusters are presented, indicating that correlations among intracluster properties contain cosmological information beyond that encoded in the cluster abundance alone, which can be captured by machine learning trained on multi-cosmology hydrodynamical simulations.

Abstract

Context: We present the first Cosmological Parameter inferences from eROSITA X-ray observations of galaxy clusters using a Machine Learning algorithm. Methods: We train a Random Forest using mock catalogs of clusters from Magneticum multi-cosmology hydrodynamical simulations. We apply the trained ML algorithm to observed X-ray features (gas luminosity, mass, and temperature) at different redshifts from the eROSITA eFEDS and eRASS1 catalogs. Results: We obtain cosmological constraints with precision comparable to those from standard analyses, such as weak lensing and cluster abundances. We infer $Ω_{\rm m}=0.30^{+0.03}_{-0.02}$, $σ_8=0.81\pm0.01$, and $h_0=0.710\pm0.004$. The recovered parameters show no tension in the $Ω_{\rm m}-σ_8$ space, but a significant deviation of $h_0$ from the Planck estimates. These inferences remain rather stable against variations of the input observable set and parameter space coverage. These results indicate that correlations among intracluster properties contain cosmological information beyond that encoded in the cluster abundance alone, which can be captured by machine learning trained on multi-cosmology simulations. Conclusions: ML algorithms trained on multi-cosmology hydrodynamical simulations can effectively infer cosmological parameters directly from galaxy cluster data. This is a change of paradigm in the context of cosmological parameter inferences. This approach complements traditional cluster-count analyses and is particularly suited to large upcoming surveys, where systematic uncertainties in mass calibration may otherwise dominate the error budget. It also highlights the potential of large-scale X-ray surveys to deliver independent tests of the standard cosmological model.

Figures (12)

• Figure 1: Galaxy cluster counts and redshift distribution of 15 MR simulations.
• Figure 2: Original, no cut-off, and no selection-weighted distribution of redshift and luminosity of the eROSITA cluster sample, along with the selection function used in Eq. \ref{['eq: selection fun']}. The probability is indicated by the dashed line, and the 16, 50, and 84 percent level contours of galaxy clusters are indicated by the solid line.
• Figure 3: Final properties of the galaxy cluster samples after cleaning: feature density distributions $(R_{500}, M_\mathrm{gas}, L_\mathrm{gas}, T_\mathrm{gas}, z)$ from the 13 Magneticum simulations (Sim) and the eROSITA observed eFEDS 2022AA...661A...7B and eRASS1 2024AA...685A.106B catalogs, respectively. They are restricted to the overlapping region for effective training and inference.
• Figure 4: Confusion matrix of the $RF$ model. Along the x-axis, the reference simulations are labeled as $\rm C\textit{i}$, $i=3...15$, as C1 and C2 from the original Magneticum simulation suite are excluded because they provide too few clusters in the corresponding volume. On the y-axis, we report the classification prediction corresponding to the x-axis.
• Figure 5: Constraints on cosmological parameters $\Omega_\mathrm{m}$, $\sigma_8$, $\Omega_\mathrm{b}$, and $h_0$ derived from eROSITA clusters by the fiducial model. Dark and light shaded contours correspond to the 68% (1$\sigma$) and 95% (2$\sigma$) confidence intervals, respectively. Constraints from 2020AA...641A...6P are included as red points and shaded regions, for comparison. Median values and the first and third quartiles are shown as dashed lines, and errors on the median parameter for the posterior marginalized probabilities are on top of each panel.