A new measure for cosmic shear

Cosmic shear, i.e., the distortion of images of high-redshift galaxies through the tidal gravitational field of the large-scale matter distribution in the Universe, offers the opportunity to measure the power spectrum of the cosmic density fluctuations without any reference to the relation of dark matter to luminous tracers. We consider here a new statistical measure for cosmic shear, the aperture mass Map(θ), which is defined as a spatially filtered projected density field and which can be measured directly from the image distortions of high-redshift galaxies. By selecting an appropriate spatial filter function, the dispersion of the aperture mass is a convolution of the power spectrum of the projected density field with a narrow kernel, so that 〈Map(θ) 〉 provides a well localized estimate of the power spectrum at wavenumbers s ∼ 5/θ. We calculate 〈 M2 〉 ap for various cosmological models, using the fully non-linear power spectrum of the cosmic density fluctuations. The non-linear evolution yields a significant increase of 〈 M2 〉 ap