Weak Lensing Peaks in Simulated Light-Cones: Investigating the Coupling
  between Dark Matter and Dark Energy
  In this paper, we study the statistical properties of weak lensing peaks in
light-cones generated from cosmological simulations. In order to assess the
prospects of such observable as a cosmological probe, we consider simulations
that include interacting Dark Energy (hereafter DE) models with coupling term
between DE and Dark Matter. Cosmological models that produce a larger
population of massive clusters have more numerous high signal-to-noise peaks;
among models with comparable numbers of clusters those with more concentrated
haloes produce more peaks. The most extreme model under investigation shows a
difference in peak counts of about $20\%$ with respect to the reference
$\mathrm{\Lambda}$CDM model. We find that peak statistics can be used to
distinguish a coupling DE model from a reference one with the same power
spectrum normalisation. The differences in the expansion history and the growth
rate of structure formation are reflected in their halo counts, non-linear
scale features and, through them, in the properties of the lensing peaks. For a
source redshift distribution consistent with the expectations of future
space-based wide field surveys, we find that typically seventy percent of the
cluster population contributes to weak-lensing peaks with signal-to-noise
ratios larger than two, and that the fraction of clusters in peaks approaches
one-hundred percent for haloes with redshift z$\leq$0.5. Our analysis
demonstrates that peak statistics are an important tool for disentangling DE
models by accurately tracing the structure formation processes as a function of
the cosmic time.
