Cosmological forecasts with the clustering of weak lensing peaks

Maximizing the information that can be extracted from weak lensing (WL) measurements is a key goal for upcoming stage IV surveys. This is typically achieved through statistics that are complementary to the cosmic shear two-point correlation function, the most well established of which is the WL peak abundance. In this work, we study the clustering of WL peaks, and present parameter constraint forecasts for an LSST-like survey. We use the cosmo-SLICS wCDM simulations to measure the peak two-point correlation function for a range of cosmological parameters, and use the simulation data to train a Gaussian process regression emulator that is applied to generate likelihood contours and provide parameter constraint forecasts from mock observations. We investigate the dependence of the peak two-point correlation function on the peak height, and find that the clustering of low-amplitude peaks is complementary to that of high-amplitude peaks. Consequently, their combination gives significantly tighter constraints than the clustering of high peaks alone. The peak two-point correlation function is significantly more sensitive to the cosmological parameters h and w₀ than the peak abundance, and when the probes are combined, constraints on Ω_m, S₈, h, and w₀ improve by at least a factor of 2, relative to the peak abundance alone. Finally, we compare the forecasts for WL peaks and voids, and show that the two are also complementary; both probes can offer better constraints on S₈ and w₀ than the shear correlation function by roughly a factor of 2.