Numerical Investigations of Weak Lensing by Large-Scale Structure

We use numerical simulations of ray tracing through N-body simulations to investigate weak lensing by large-scale structure. These are needed for testing the analytic predictions of two-point correlators, to set error estimates on them and to investigate nonlinear gravitational effects in the weak lensing maps. On scales larger than 1 degree gaussian statistics suffice and can be used to estimate the sampling, noise and aliasing errors on the measured power spectrum. For this case we describe a minimum variance inversion procedure from the 2-d to 3-d power spectrum and discuss a sparse sampling strategy which optimizes the signal to noise on the power spectrum. On degree scales and smaller the shear and convergence statistics lie in the nonlinear regime and have a non-gaussian distribution. For this regime ray tracing simulations are useful to provide reliable error estimates and calibration of the measurements. We show how the skewness and kurtosis can in principle be used to probe the mean density in the universe, but are sensitive to sampling errors and require large observed areas. The probability distribution function is likely to be more useful as a tool to investigate nonlinear effects. In particular, it shows striking differences between models with different values of the mean density $\Omega_m$.