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BSTRACT [ABSTRACT FROM AUTHOR]

Analytical expressions for covariances of weak lensing statistics related to the aperture mass, , are derived for realistic survey geometries such as the Supernova Acceleration Probe (SNAP) for a range of smoothing angles and redshift bins. We incorporate the contributions to the noise due to the intrinsic ellipticity distribution and the effects of the finite catalogue size. Extending previous results to the most general case where the overlap of source populations is included in a complete analysis of error estimates, we study how various angular scales in various redshifts are correlated and how the estimation scatter changes with the survey parameters. Dependences on cosmological parameters and source redshift distributions are studied in detail. Numerical simulations are used to test the validity of various ingredients to our calculations. Correlation coefficients are defined in a way that makes them practically independent of cosmology. They can provide important tools to cross-correlate one or more different surveys, as well as various redshift bins within the same survey or various angular scales from the same or different surveys. The dependence of these coefficients on various models of underlying mass correlation hierarchy is also studied. Generalizations of these coefficients at the level of three-point statistics have the potential of probing the complete shape dependence of the underlying bi-spectrum of the matter distribution. A complete error analysis incorporating all sources of errors suggests encouraging results for studies using future space-based weak lensing surveys such as SNAP. [ABSTRACT FROM AUTHOR]

The present generation of weak lensing surveys will be superseded by surveys run from space with much better sky coverage and high level of signal-to-noise ratio, such as theSupernova/Acceleration Probe(SNAP). However, removal of any systematics or noise will remain a major cause of concern for any weak lensing survey. One of the best ways of spotting any undetected source of systematic noise is to compare surveys that probe the same part of the sky. In this paper we study various measures that are useful in cross-correlating weak lensing surveys with diverse survey strategies. Using two different statistics– the shear components and the aperture mass– we construct a class of estimators which encode such cross-correlations. These techniques will also be useful in studies where the entire source population from a specific survey can be divided into various redshift bins to study cross-correlations among them. We perform a detailed study of the angular size dependence and redshift dependence of these observables and of their sensitivity to the background cosmology. We find that one-point and two-point statistics provide complementary tools which allow one to constrain cosmological parameters and to obtain a simple estimate of the noise of the survey. [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]

We describe the predictions for the smoothed weak lensing shear, , and aperture mass, , of two simple analytical models of the density field: the minimal tree model and the stellar model. Both models give identical results for the statistics of the three-dimensional density contrast smoothed over spherical cells and only differ by the detailed angular dependence of the many-body density correlations. We have shown in previous work that they also yield almost identical results for the probability distribution function (PDF) of the smoothed convergence, . We find that the two models give rather close results for both the shear and the positive tail of the aperture mass. However, we note that at small angular scales the tail of the PDF, , for negative shows a strong variation between the two models, and the stellar model actually breaks down for and . This shows that the statistics of the aperture mass provides a very precise probe of the detailed structure of the density field, as it is sensitive to both the amplitude and the detailed angular behaviour of the many-body correlations. On the other hand, the minimal tree model shows good agreement with numerical simulations over all the scales and redshifts of interest, while both models provide a good description of the PDF, , of the smoothed shear components. Therefore, the shear and the aperture mass provide robust and complementary tools to measure the cosmological parameters as well as the detailed statistical properties of the density field. [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]