Power spectrum from weak-shear data

We demonstrate that the aperture mass as a measure for cosmic shear closely approximates (to better than approximate to 5%) the scaled and shifted pow er spectrum of the projected mass density. This cosmological weak-lensing i nformation can thus be used to directly infer the projected matter power sp ectrum with high accuracy. As an application, we show that aperture-mass ob servations can be used to constrain the cosmic density parameter and the po wer-spectrum amplitude. We show that, for a particular example, it should b e possible to constrain Omega(0) to within approximate to +/-27%, and sigma (8) to within approximate to +/-8% using weak-shear data on a square-shaped field of 8 degrees side length.