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We study various measures of weak-lensing distortions in future surveys, taking into account the noise arising from the finite survey size and the intrinsic ellipticity of galaxies. We also consider a realistic redshift distribution of the sources, as expected for theSNAPmission. We focus on the low-order moments and the full distribution function (PDF) of the aperture massMap and of the smoothed shear component. We also propose new unbiased estimators for low-order cumulants which have less scatter than the usual estimators of non-Gaussianity based on the moments themselves. Then, using an analytical model which has already been seen to provide a good description of weak gravitational lensing through a comparison with numerical simulations, we study the statistical measures that can be extracted from future surveys such as theSNAPexperiment. We recover the fact that at small angular scalesthe variance can be extracted with an accuracy of a few per cent. Non-Gaussianity can also be measured from the skewness of the aperture mass (at a 10 per cent level), while the shear kurtosis is more noisy and cannot be easily measured beyond 6 arcmin. On the other hand, we find that the PDF of the estimator associated with the aperture mass can be distinguished both from the Gaussian and the Edgeworth expansion and could provide useful constraints, while this appears to be difficult to realize with the shear component. Finally, we investigate various survey strategies and the possibility of performing a redshift binning of the sample. [ABSTRACT FROM AUTHOR]

The one-point probability distribution function (pdf) of the large-scale density field is an important tool to follow the evolution of cosmological structures. In this paper we present a new model for this pdf for all regimes and all densities, that is from linear to highly non-linear scales and from rare voids up to rare high densities. This is probably the simplest model one can build which is consistent with normalization constraints and known rigorous results (the quasi-linear regime and the rare void limit). It is fully parametrized by the non-linear variance and skewness. We obtain a good agreement withN-body data from realistic cosmological simulations of the Virgo Consortium and we find that it works significantly better than previous models such as the lognormal model or the extended perturbation theory. We explain this success as a result of the tight constraints on to the pdf provided by these consistency conditions. We also point out that while the Lagrangian dynamics of typical fluctuations is quite complex, the statistical outcome seems rather simple. This simple model should be useful for studies which require a realistic and convenient description of this pdf. [ABSTRACT FROM AUTHOR]

Weak gravitational lensing surveys are rapidly becoming important tools to probe directly the mass density fluctuations in the Universe and its background dynamics. Earlier studies have shown that it is possible to model the statistics of the convergence field on small angular scales by suitably modelling the statistics of the underlying density field in the highly non-linear regime. We extend such methods to model the complete probability distribution function of the shear as a function of smoothing angle. Our model relies on a simple hierarchical Ansatz for the behaviour of the higher-order correlations in the density field. We compare our predictions with the results of numerical simulations and find excellent agreement for different cosmological scenarios. Our method provides a new way to study the evolution of non-Gaussianity in gravitational clustering and should help to break the degeneracies in parameter estimation based on analysis of the power spectrum alone. [ABSTRACT FROM AUTHOR]

Weak-lensing convergence can be used directly to map and probe the dark-mass distribution in the Universe. Building on earlier studies, we recall how the statistics of the convergence field are related to the statistics of the underlying mass distribution, in particular to the many-body density correlations. We describe two model-independent approximations which provide two simple methods to compute the probability distribution function (pdf) of the convergence. We apply one of these to the case where the density field can be described by a lognormal pdf. Next, we discuss two hierarchical models for the high-order correlations which allow us to perform exact calculations and evaluate the previous approximations in such specific cases. Finally, we apply these methods to a very simple model for the evolution of the density field from linear to highly non-linear scales. Comparisons with the results obtained from numerical simulations, obtained from a number of different realizations, show excellent agreement with our theoretical predictions. We have probed various angular scales in the numerical work and considered sources at 14 different redshifts in each of two different cosmological scenarios, an open cosmology and a flat cosmology with non-zero cosmological constant. Our simulation technique employs computations of the full three-dimensional shear matrices along the line of sight from the source redshift to the observer and is complementary to more popular ray-tracing algorithms. Our results therefore provide a valuable cross-check for such complementary simulation techniques, as well as for our simple analytical model, from the linear to the highly non-linear regime. [ABSTRACT FROM AUTHOR]