The FLAMINGO project: cosmology with the redshift dependence of weak gravitational lensing peaks

Weak gravitational lensing (WL) convergence peaks contain valuable cosmological information in the regime of non-linear collapse. Using the FLAMINGO suite of cosmological hydrodynamical simulations, we study the physical origin and redshift distributions of the objects generating WL peaks selected from a WL convergence map mimicking a $\textit{Euclid}$ signal. We match peaks to individual haloes and show that the high signal-to-noise ratio (SNR$~>~5$) WL peaks measured by Stage IV WL surveys primarily trace $M_{\mathrm{200c}} > 10^{14}~\mathrm{M_\odot}$ haloes. We find that the WL peak sample can compete with the purity and completeness of state-of-the-art X-ray and Sunyaev-Zel'dovich cluster abundance inferences. By comparing the distributions predicted by simulation variations that have been calibrated to the observed gas fractions of local clusters and the present-day galaxy stellar mass function, or shifted versions of these, we illustrate that the shape of the redshift distribution of SNR$~>~5$ peaks is insensitive to baryonic physics while it does change with cosmology. The difference highlights the potential of using WL peaks to constrain cosmology. As the WL convergence and redshift number densities of WL peaks scale differently with cosmology and baryonic feedback, WL peak statistics can simultaneously calibrate baryonic feedback and constrain cosmology.