Cosmology with Minkowski functionals and moments of the weak lensing convergence field

Abstract

We compare the efficiency of moments and Minkowski functionals (MFs) in constraining the subset of cosmological parameters $({\ensuremath{\Omega}}_{m},w,{\ensuremath{\sigma}}_{8})$ using simulated weak lensing convergence maps. We study an analytic perturbative expansion of the MFs [T. Matsubara, Phys. Rev. D 81, 083505 (2010); D. Munshi et al., Mon. Not. R. Astron. Soc. 419, 536 (2012)] 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 ${5}^{\ensuremath{'}}$, while it shows a good degree of convergence on larger scales ($\ensuremath{\sim}{15}^{\ensuremath{'}}$). 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 ${1}^{\ensuremath{'}}$, 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 a set of either these moments or the MFs can significantly tighten constraints on cosmological parameters, compared to the conventional method of using the power spectrum alone.