The cosmological information of shear peaks: beyond the abundance
  We study the cosmological information of weak lensing (WL) peaks, focusing on
two other statistics besides their abundance: the stacked tangential-shear
profiles and the peak-peak correlation function. We use a large ensemble of
simulated WL maps with survey specifications relevant to future missions like
Euclid and LSST, to explore the three peak probes. We find that the correlation
function of peaks with high signal-to-noise (S/N) measured from fields of size
144 sq. deg. has a maximum of ~0.3 at an angular scale ~10 arcmin. For peaks
with smaller S/N, the amplitude of the correlation function decreases, and its
maximum occurs on smaller angular scales. We compare the peak observables
measured with and without shape noise and find that for S/N~3 only ~5% of the
peaks are due to large-scale structures, the rest being generated by shape
noise. The covariance matrix of the probes is examined: the correlation
function is only weakly covariant on scales < 30 arcmin, and slightly more on
larger scales; the shear profiles are very correlated for theta > 2 arcmin,
with a correlation coefficient as high as 0.7. Using the Fisher-matrix
formalism, we compute the cosmological constraints for {Om_m, sig_8, w, n_s}
considering each probe separately, as well as in combination. We find that the
correlation function of peaks and shear profiles yield marginalized errors
which are larger by a factor of 2-4 for {Om_m, sig_8} than the errors yielded
by the peak abundance alone, while the errors for {w, n_s} are similar. By
combining the three probes, the marginalized constraints are tightened by a
factor of ~2 compared to the peak abundance alone, the least contributor to the
error reduction being the correlation function. This work therefore recommends
that future WL surveys use shear peaks beyond their abundance in order to
constrain the cosmological model.
