Impact of non-Gaussian likelihood on cosmological constraints from the thermal Sunyaev--Zel'dovich power spectrum: a simulation-based inference analysis
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 \textit{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 $\ell < 1000$, 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 \textit{Planck}-like tSZ analysis, while SBI provides a useful validation tool to model non-Gaussian likelihoods beyond analytic approximations.