Constraining cosmology with thermal Sunyaev-Zel'dovich maps: Minkowski functionals, peaks, minima, and moments

The thermal Sunyaev-Zel'dovich effect (tSZ) is a sensitive probe of cosmology, as it traces the abundance of galaxy clusters and groups in the late-time Universe. Upcoming cosmic microwave background experiments such as the Simons Observatory (SO) and CMB-S4 will provide low-noise and high-resolution component-separated tSZ maps covering a large sky fraction. The tSZ signal is highly non-Gaussian; therefore, higher-order statistics are needed to optimally extract information from these maps. In this work, we study the cosmological constraining power of several tSZ statistics -- Minkowski functionals (MFs), peaks, minima, and moments -- that have yielded promising results in capturing non-Gaussian information from other cosmological data. Using a large suite of halo-model-based tSZ simulations with varying $\Omega_{c}$ and $\sigma_{8}$ (154 cosmologies and over $800, 000$ maps, each $10.5\times10.5$ deg$^{2}$), we show that by combining these observables, we can achieve $\approx 29\times$ tighter constraints compared to using the tSZ power spectrum alone in an idealized noiseless case, with the MFs dominating the constraints. We show that much of the MF constraining power arises from halos below the detection threshold of cluster surveys, suggesting promising synergies with cluster-count analyses. Finally, we demonstrate that these statistics have the potential to deliver tight constraints even in the presence of noise. For example, using post-component-separation tSZ noise expected for SO, we obtain $\approx1.6\times$ and $\approx1.8\times$ tighter constraints than the power spectrum with MFs and all statistics combined, respectively. We show that the constraints from MFs approach the noiseless case for white-noise levels $\lesssim 1 \,\, \mu$K-arcmin.