Context. Weak gravitational lensing is a powerful probe oflarge-scale structure and cosmology. Most commonly, second-ordercorrelations of observed galaxy ellipticities are expressed as aprojection of the matter power spectrum, corresponding to thelowest-order approximation between the projected and thethree-dimensional power spectrum. Aims. The dominant lensing-only contribution beyond thezero-order approximation is the reduced shear, which takes into accountnot only lensing-induced distortions but also the isotropicmagnification of galaxy images. This involves an integral over thematter bispectrum. We provide a fast and general way to calculate thiscorrection term. Methods. Using a model for the matter bispectrum, we fitelementary functions to the reduced-shear contribution and itsderivatives with respect to cosmological parameters. The dependence oncosmology is encompassed in a Taylor-expansion around a fiducial model.Results. Within a region in parameter space comprising the WMAP768% error ellipsoid, the total reduced-shear power spectrum (shear plusfitted reduced-shear correction) is accurate to 1% (2%) for ().This corresponds to a factor of four reduction in the bias compared tothe case where no correction is used. This precision is necessary tomatch the accuracy of current non-linear power spectrum predictionsfrom numerical simulations. Key words: gravitational lensing: weak - large-scale structure of Universe
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