Cosmological forecasts with the clustering of weak lensing peaks
  Maximising the information that can be extracted from weak lensing
measurements is a key goal for upcoming surveys such as LSST and Euclid. 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
weak lensing peak abundance. In this work, we study the clustering of weak
lensing peaks, and present parameter constraint forecasts for an LSST-like
survey. We use the cosmoslics $w$CDM 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 which 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 $w_0$ than
the 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 for
weak lensing peaks and weak lensing voids, and show that the two are also
complementary; both probes can offer better constraints on $S_8$ and $w_0$ than
the shear correlation function by roughly a factor of two.
