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Impact of non-Gaussian likelihood on cosmological constraints from the thermal Sunyaev-Zel’dovich power spectrum: A simulation-based inference analysis

Licong Xu1,2,*, Íñigo Zubeldia1,2,3, James Alvey1,2, Boris Bolliet4,2, and Anthony Challinor1,2,3

  • 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
  • 3DAMTP, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
  • 4Cavendish Astrophysics, University of Cambridge, Madingley Road, Cambridge CB3 0HA, United Kingdom

  • *Contact author: lx256@cam.ac.uk
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Phys. Rev. D 114, 043528 – Published 14 August, 2026

DOI: https://doi.org/10.1103/tl9p-ldwf

Abstract

The thermal Sunyaev–Zel’dovich (tSZ) power spectrum is a sensitive probe of cosmology and cluster astrophysics, but its statistics are non-Gaussian because the signal receives a significant contribution from rare, massive, low-redshift galaxy clusters. As a result, a Gaussian likelihood fails to describe the statistics of its power spectrum on large scales. We use simulation-based inference (SBI) to test the accuracy of the standard Gaussian power-spectrum likelihood for a Planck-like tSZ analysis. Using halo-based simulations of full-sky Compton-y maps, we train neural posterior and likelihood estimators and compare the resulting constraints with those from a Gaussian likelihood assumption. Using only multipoles ℓ<1000, we find that the Gaussian likelihood assumption gives unbiased cosmological constraints, while the SBI-based inference shows a mild broadening of the posterior distributions for the amplitudes of residual foregrounds. This suggests that the Gaussian likelihood assumption is sufficiently accurate for cosmological inference for a Planck-like tSZ analysis, while SBI provides a useful validation tool to model non-Gaussian likelihoods beyond analytic approximations.

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Phys. Rev. D 114, 043528– Published 14 August, 2026
  • Received 12 June 2026
  • Accepted 14 July 2026
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