P. Valageas, Statistical properties of the convergence due to weak gravitational lensing by non-linear structures, ASTRON ASTR, 356(3), 2000, pp. 771-787
Density fluctuations in the matter distribution lead to distortions of the
images of distant galaxies through weak gravitational lensing effects. This
provides an efficient probe of the cosmological parameters and of the dens
ity field. In this article, we investigate the statistical properties of th
e convergence due to weak gravitational lensing by non-linear structures (i
.e. we consider small angular windows theta less than or similar to 1'). Pr
evious studies have shown how to relate the second and third order moments
of the convergence to those of the density contrast while models based on t
he Press-Schechter prescription provide an estimate of the tail of P(kappa)
. Here we present a method to obtain nn estimate of the full p.d.f. of the
convergence kappa. It is based on a realistic description of the density fi
eld which applies to overdense as well as underdense regions. We show that
our predictions agree very well with the results of N-body simulations for
the convergence. This could allow one to derive the cosmological parameters
(Omega(m), Omega(Lambda)) as well as the full p.d.f. P(delta(R)) of the de
nsity contrast itself in the non-linear regime from observations. Hence thi
s gives a very powerful tool to constrain scenarios of structure formation.