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 run 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 512³ N-body runs, covering seven different cosmologies, varying three cosmological parameters Ωₘ, w, and σ₈ one at a time, around a fiducial lambda cold dark matter model. In each cosmology, we use ray tracing to create a thousand pseudoindependent 12 deg² 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 zₛ=1, 1.5, 2, explore five different smoothing scales θG=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 V₀, the ``area'' MF), and partly through nonlinear spatial information (through combining different smoothing scales for V₀, and through V₁ and V₂, 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.