Fitting formulae of the reduced-shear power spectrum for weak lensing

TL;DR

This paper introduces a fast, accurate method to compute the reduced-shear correction in weak lensing power spectra, significantly reducing bias and improving precision for cosmological analyses.

Contribution

It provides a novel fitting formula for the reduced-shear correction, enabling efficient and precise calculations across relevant cosmological parameter ranges.

Findings

Achieves 1% accuracy for l<10^4 within WMAP7 error ellipsoid

Reduces bias by a factor of four when including the correction

Matches the precision of current non-linear power spectrum predictions

Abstract

Context. Weak gravitational lensing is a powerful probe of large-scale structure and cosmology. Most commonly, second-order correlations of observed galaxy ellipticities are expressed as a projection of the matter power spectrum, corresponding to the lowest-order approximation between the projected and 3d power spectrum. Aims. The dominant lensing-only contribution beyond the zero-order approximation is the reduced shear, which takes into account not only lensing-induced distortions but also isotropic magnification of galaxy images. This involves an integral over the matter bispectrum. We provide a fast and general way to calculate this correction term. Methods. Using a model for the matter bispectrum, we fit elementary functions to the reduced-shear contribution and its derivatives with respect to cosmological parameters. The dependence on cosmology is encompassed in a Taylor-expansion around a fiducial model. Results. Within a region in parameter space comprising the WMAP7 68% error ellipsoid, the total reduced-shear power spectrum (shear plus fitted reduced-shear correction) is accurate to 1% (2%) for l<10^4 (l<2x10^5). This corresponds to a factor of four reduction of the bias compared to the case where no correction is used. This precision is necessary to match the accuracy of current non-linear power spectrum predictions from numerical simulations.