Weak lensing by large-scale structure in open, flat and closed universes

Weak lensing is the distortion (polarization) of images of distant objects,such as high redshift galaxies, by gravitational fields in the limit where thedistortion is small. Gravitational potential fluctuations due to large scalestructure cause correlated distortions of the images of high redshift galaxies.These distortions are observable with current large telescopes andinstrumentation. In a Friedmann-Robertson-Walker (FRW) metric I calculate theweak lensing pattern due to large scale structure for arbitrary $\Omega_0$ andzero cosmological constant $\Lambda$. For a given cosmological model, specifiedby $\Omega_0$ and a power spectrum of density fluctuations, I calculate thestatistical properties of the polarization field for an arbitrary redshiftsource distribution in a simple closed form. It is shown that for low redshift$z$ of the sources, the polarization amplitude is proportional to $\Omega_0$,while at higher redshift the polarization measures the value of $\Omega(z)$,where $z$ is the characteristic source redshift. Moreover, the statistics ofthe polarization field are a direct measure of the power spectrum of densityfluctuations.Comment: uuencoded compressed postscript fil