Weak lensing and cosmology

Recently, it has been shown that it is possible to reconstruct the projected mass distribution of a cluster from weak lensing provided that both the geometry of the universe and the probability distribution of galaxy redshifts are known; actually, when additional photometric data are taken to be available, the galaxy redshift distribution could be determined jointly with the cluster mass from the weak lensing analysis. In this paper we develop, in the spirit of a ``thought experiment,'' a method to constrain the geometry of the universe from weak lensing, provided that the redshifts of the source galaxies are measured. The quantitative limits and merits of the method are discussed analytically and with a set of simulations, in relation to point estimation, interval estimation, and test of hypotheses for homogeneous Friedmann-Lema\^\i tre models. The constraints turn out to be significant when a few thousand source galaxies are used.