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Extracting cosmological information from the abundance of galaxy clusters with simulation-based inference

Íñigo Zubeldia1,2,*, Boris Bolliet3,2, Anthony Challinor1,2,4, and William Handley1,2

  • 1Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, United Kingdom
  • 2Kavli Institute for Cosmology, University of Cambridge, Madingley Road, Cambridge CB3 0HA, United Kingdom
  • 3Cavendish Astrophysics, University of Cambridge, Madingley Road, Cambridge CB3 0HA, United Kingdom
  • 4DAMTP, Centre for Mathematical Sciences, Wilberforce Road, Cambridge, CB3 0WA, United Kingdom

  • *Contact author: inigo.zubeldia@ast.cam.ac.uk
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Phys. Rev. D 112, 083536 – Published 17 October, 2025

DOI: https://doi.org/10.1103/drn7-ggqk

Abstract

The abundance of galaxy clusters as a function of mass and redshift is a well-established and powerful cosmological probe. Cosmological analyses based on galaxy cluster number counts have traditionally relied on explicitly computed likelihoods, which are often challenging to develop with the required accuracy and expensive to evaluate. In this work, we implement an alternative approach based on simulation-based inference (SBI) methods that relies solely on synthetic galaxy cluster catalogs generated under a given model. These catalogs are much easier to produce than it is to develop and validate a likelihood. We validate this approach in the context of the galaxy cluster survey of the upcoming Simons Observatory for a setup in which we can also evaluate an exact explicit likelihood. We find that our SBI-based approach yields cosmological parameter posterior means that are within 0.2σ of those obtained with the explicit likelihood and with biases smaller than 0.1σ. We also introduce and validate a procedure to assess the goodness of fit using only synthetic catalogs similar to those used for training. This demonstrates, for the first time, that a galaxy cluster number count cosmological analysis can be performed fully without resorting to a likelihood at any stage. Finally, we apply our SBI-based approach to the real Planck MMF3 cosmology sample, obtaining cosmological parameter constraints that are within 0.1σ of their likelihood-based counterparts. This constitutes the first SBI-based number count cosmological analysis of a real galaxy cluster catalog.

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Phys. Rev. D 112, 083536– Published 17 October, 2025
  • Received 14 April 2025
  • Accepted 18 September 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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