Probing Cosmology with Weak Lensing Minkowski Functionals
  In this paper, we show that Minkowski Functionals (MFs) of weak gravitational
lensing (WL) convergence maps contain significant non-Gaussian,
cosmology-dependent information. To do this, we use a large suite of
cosmological ray-tracing N-body simulations to create mock WL convergence maps,
and study the cosmological information content of MFs derived from these maps.
Our suite consists of 80 independent 512^3 N-body runs, covering seven
different cosmologies, varying three cosmological parameters Omega_m, w, and
sigma_8 one at a time, around a fiducial LambdaCDM model. In each cosmology, we
use ray-tracing to create a thousand pseudo-independent 12 deg^2 convergence
maps, and use these in a Monte Carlo procedure to estimate the joint confidence
contours on the above three parameters. We include redshift tomography at three
different source redshifts z_s=1, 1.5, 2, explore five different smoothing
scales theta_G=1, 2, 3, 5, 10 arcmin, and explicitly compare and combine the
MFs with the WL power spectrum. We find that the MFs capture a substantial
amount of information from non-Gaussian features of convergence maps, i.e.
beyond the power spectrum. The MFs are particularly well suited to break
degeneracies and to constrain the dark energy equation of state parameter w (by
a factor of ~ three better than from the power spectrum alone). The
non-Gaussian information derives partly from the one-point function of the
convergence (through V_0, the "area" MF), and partly through non-linear spatial
information (through combining different smoothing scales for V_0, and through
V_1 and V_2, the boundary length and genus MFs, respectively). In contrast to
the power spectrum, the best constraints from the MFs are obtained only when
multiple smoothing scales are combined.
