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-Lemaitre models. The constraints turn out to be significant when a
few thousand source galaxies are used.Comment: 17 pages, 8 figures. Uses A&A LaTeX style. Accepted for pubblication
by A&A. Several changes made: new model for the lens; Sect. 7 and App. A.
adde
