Simulation-based cosmological inference from optically selected galaxy clusters with Capish

¹ Université Paris-Saclay, CEA, IRFU, 91191 Gif-sur-Yvette, France
² Université Paris Cité, CNRS-IN2P3, APC, 75013 Paris, France

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 5 February 2026
Accepted: 15 May 2026

Abstract

Galaxy clusters are powerful probes of the growth of cosmic structure through measurements of their abundance as a function of mass and redshift. Extracting precise cosmological constraints from cluster surveys is challenging, as we must contend with nontrivial correlations between lensing mass and optical richness, as well as the complex relationship between richness and the underlying halo mass. These difficulties are compounded by systematic effects such as selection function biases, super-sample covariance, and correlated measurement noise between mass proxies. As upcoming photometric surveys are expected to detect tens to hundreds of thousands of galaxy clusters, controlling these systematics becomes essential. In this paper, we present a forward-modeling approach using simulation-based inference (SBI), which provides a natural framework for jointly modeling cluster abundance and lensing mass observables while capturing systematic uncertainties at higher fidelity than analytic likelihood methods – which rely on simplifying assumptions such as fixed covariances and Gaussianity – without requiring an explicit likelihood formulation. We introduce Capish, a Python code for generating forward-modeled galaxy cluster catalogs using halo mass functions and incorporating observational effects. We perform SBI using neural density estimation with normalizing flows, trained on abundance and mean lensing mass measurements in observed redshift–richness bins. Key cluster-related summary statistics measured on Capish simulations faithfully reproduce their corresponding analytical predictions, and we perform several Bayesian robustness tests of posterior modeling. Our forward model accounts for realistic noise, redshift uncertainties, selection functions, and correlated scatter between lensing mass and observed richness. We find good agreement with explicit-likelihood analyzes, with broader SBI posteriors reflecting the increased realism of the forward model. We also test Capish on cluster catalogs built from a large cosmological simulation, finding a good fit to the cosmological parameters.