Theory and statistics of weak lensing from large-scale mass inhomogeneities

Weak lensing by large-scale mass inhomogeneities in the Universe induces co rrelations in the observed ellipticities of distant sources. We first revie w the harmonic analysis and statistics required of these correlations and d iscuss calculations for the predicted signal. We consider the ellipticity c orrelation function, the mean-square ellipticity, the ellipticity power spe ctrum and a global maximum-likelihood analysis to isolate a weak-lensing si gnal from the data. Estimates for the sensitivity of a survey of a given ar ea, surface density, and mean intrinsic source ellipticity are presented. W e then apply our results to the FIRST radio-source survey. We predict an rm s ellipticity of roughly 0.011 in 1 x 1 deg(2) pixels and 0.018 in 20 x 20 arcmin(2) pixels if the power spectrum is normalized to sigma(8)Omega(0.53) = 0.6, as indicated by the cluster abundance. The signal is significantly larger in some models if the power spectrum is normalized instead to the CO BE anisotropy. The uncertainty in the predictions from imprecise knowledge of the FIRST redshift distribution is about 25 per cent in the rms elliptic ity. We show that FIRST should be able to make a statistically significant detection of a weak-lensing signal for cluster-abundance-normalized power s pectra.