Cosmology Constraints from the Weak Lensing Peak Counts and the Power
  Spectrum in CFHTLenS
  Lensing peaks have been proposed as a useful statistic, containing
cosmological information from non-Gaussianities that is inaccessible from
traditional two-point statistics such as the power spectrum or two-point
correlation functions. Here we examine constraints on cosmological parameters
from weak lensing peak counts, using the publicly available data from the 154
deg$^2$ CFHTLenS survey. We utilize a new suite of ray-tracing N-body
simulations on a grid of 91 cosmological models, covering broad ranges of the
three parameters $\Omega_m$, $\sigma_8$, and $w$, and replicating the Galaxy
sky positions, redshifts, and shape noise in the CFHTLenS observations. We then
build an emulator that interpolates the power spectrum and the peak counts to
an accuracy of $\leq 5\%$, and compute the likelihood in the three-dimensional
parameter space ($\Omega_m$, $\sigma_8$, $w$) from both observables. We find
that constraints from peak counts are comparable to those from the power
spectrum, and somewhat tighter when different smoothing scales are combined.
Neither observable can constrain $w$ without external data. When the power
spectrum and peak counts are combined, the area of the error "banana'' in the
($\Omega_m$, $\sigma_8$) plane reduces by a factor of $\approx2$, compared to
using the power spectrum alone. For a flat $\Lambda$ cold dark matter model,
combining both statistics, we obtain the constraint
$\sigma_8(\Omega_m/0.27)^{0.63}=0.85\substack{+0.03 \\ -0.03}$.
