Cosmology with Minkowski functionals and moments of the weak lensing
  convergence field
  We compare the efficiency of moments and Minkowski functionals (MFs) in
constraining the subset of cosmological parameters (Omega_m,w,sigma_8) using
simulated weak lensing convergence maps. We study an analytic perturbative
expansion of the MFs in terms of the moments of the convergence field and of
its spatial derivatives. We show that this perturbation series breaks down on
smoothing scales below 5', while it shows a good degree of convergence on
larger scales (15'). Most of the cosmological distinguishing power is lost when
the maps are smoothed on these larger scales. We also show that, on scales
comparable to 1', where the perturbation series does not converge, cosmological
constraints obtained from the MFs are approximately 1.5-2 times better than the
ones obtained from the first few moments of the convergence distribution ---
provided that the latter include spatial information, either from moments of
gradients, or by combining multiple smoothing scales. Including either a set of
these moments or the MFs can significantly tighten constraints on cosmological
parameters, compared to the conventional method of using the power spectrum
alone.
