Power spectrum from weak-shear data

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We demonstrate that the aperture mass as a measure for cosmic shear closely approximates (to better than 5%) the scaled and shifted power spectrum of the projected mass density. This cosmological weak-lensing information can thus be used to directly infer the projected matter power spectrum with high accuracy. As an application, we show that aperture-mass observations can be used to constrain the cosmic density parameter and the power-spectrum amplitude. We show that, for a particular example, it should be possible to constrain Omega₀ to within +/- 27%, and sigma₈ to within +/- 8% using weak-shear data on a square-shaped field of 8 degrees side length.