Publication : t96/108

Abstract:
The possibility of detecting weak lensing effects from deep wide field imaging surveys has open new means of probing the large-scale structures of the Universe and measuring cosmological parameters. In this paper we present a systematic study of the expected dependence of the low order moments of the filtered {\sl gravitational local convergence} with the power spectrum of the density fluctuations and with the cosmological parameters $\Omega_0$ and $\Lambda$. The results show a significant dependence with all these parameters. Though we note that this degeneracy could be partially raised by considering two populations of sources, at different redshifts, computing the third moment is more promising since it is expected, in the quasi-linear regime and for Gaussian initial conditions, to be only $\Omega_0$ dependent (with a slight degeneracy with $\Lambda$) when it is correctly expressed in terms of the second moment. More precisely we show that the variance of the convergence varies approximately as $P(k) \ \Omega_0^{1.5} \ z_s^{1.5}$, whereas the skewness varies as $\Omega_0^{-0.8} \ z_s^{-1.35}$, where $P(k)$ is the projected power spectrum and $z_s$ the redshift of sources. Thus, used jointly they can provide both $P(k)$ and $\Omega_0$. However, the dependence with the redshift of sources is large and could be a major concern for a practical implementation. %since the weakly %lensed background galaxies are very faint and well beyond the %capabilities of 10 meters telescopes. We have estimated the errors expected for these parameters in realistic scenario and sketched what would be the observational requirements for doing such measurements. A more detailed study of an observational strategy is left for a second paper.

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