We study the cosmological information contained in the Minkowski functionals (MFs) of weak gravitational lensing convergence maps. We show that the MFs provide strong constraints on the local-type primordial non-Gaussianity parameter f NL. We run a set of cosmological N-body simulations and perform ray-tracing simulations of weak lensing to generate 100 independent convergence maps of a 25?deg2 field of view for f NL = –100, 0 and 100. We perform a Fisher analysis to study the degeneracy among other cosmological parameters such as the dark energy equation of state parameter w and the fluctuation amplitude σ8. We use fully nonlinear covariance matrices evaluated from 1000 ray-tracing simulations. For upcoming wide-field observations such as those from the Subaru Hyper Suprime-Cam survey with a proposed survey area of 1500?deg2, the primordial non-Gaussianity can be constrained with a level of f NL ~ 80 and w ~ 0.036 by weak-lensing MFs. If simply scaled by the effective survey area, a 20,000?deg2 lensing survey using the Large Synoptic Survey Telescope will yield constraints of f NL ~ 25 and w ~ 0.013. We show that these constraints can be further improved by a tomographic method using source galaxies in multiple redshift bins.
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