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Maximising the information that can be extracted from weak lensingmeasurements is a key goal for upcoming surveys such as LSST and Euclid. Thisis typically achieved through statistics that are complementary to the cosmicshear two-point correlation function, the most well established of which is theweak lensing peak abundance. In this work, we study the clustering of weaklensing peaks, and present parameter constraint forecasts for an LSST-likesurvey. We use the cosmoslics $w$CDM simulations to measure the peak two-pointcorrelation function for a range of cosmological parameters, and use thesimulation data to train a Gaussian process regression emulator which isapplied to generate likelihood contours and provide parameter constraintforecasts from mock observations. We investigate the dependence of the peaktwo-point correlation function on the peak height, and find that the clusteringof low amplitude peaks is complementary to that of high amplitude peaks.Consequently, their combination gives significantly tighter constraints thanthe clustering of high peaks alone. The peak two-point correlation function issignificantly more sensitive to the cosmological parameters $h$ and $w_0$ thanthe peak abundance, and when the probes are combined, constraints on$\Omega_{\rm m}$, $S_8$, $h$ and $w_0$ improve by at least a factor of two,relative to the peak abundance alone. Finally, we compare the forecasts forweak lensing peaks and weak lensing voids, and show that the two are alsocomplementary; both probes can offer better constraints on $S_8$ and $w_0$ thanthe shear correlation function by roughly a factor of two.

Cosmological forecasts with the clustering of weak lensing peaks