Abstract

The thermal Sunyaev-Zel’dovich (tSZ) power spectrum serves as a critical probe of large-scale structure, providing sensitive constraints on the amplitude of matter fluctuations, σ_8​, and the matter density, Ω_m​. However, standard statistical analyses of this observable conventionally rely on a Gaussian likelihood approximation, an assumption that is physically challenged at large angular scales due to the Poisson nature of cluster number counts. In this talk, I will present a framework for extracting cosmological information from the tSZ power spectrum using Simulation-Based Inference (SBI) using Neural Likelihood Estimation (NLE) trained on halo-based forward models. We demonstrate that the standard Gaussian likelihood approximation yields unbiased constraints on the derived cosmological parameters, even in the presence of significant skewness in the power spectrum distribution at low multipoles. Finally, I will very briefly discuss the extensibility of our forward-modelling pipeline to alternative summary statistics, such as Cluster Number Counts (CNC) and the Wavelet Scattering Transform (WST), to better exploit the full information content of Compton-y maps.