The power spectrum of systematics in cosmic shear tomography and the bias on cosmological parameters

Cosmic shear tomography has emerged as one of the most promising tools to both investigate the nature of dark energy and discriminate between General Relativity and modified gravity theories. In order to successfully achieve these goals, systematics in shear measurements have to be taken into account; their impact on the weak lensing power spectrum has to be carefully investigated in order to estimate the bias induced on the inferred cosmological parameters. To this end, we develop here an efficient tool to compute the power spectrum of systematics by propagating, in a realistic way, shear measurement, source properties and survey setup uncertainties. Starting from analytical results for unweighted moments and general assumptions on the relation between measured and actual shear, we derive analytical expressions for the multiplicative and additive bias, showing how these terms depend not only on the shape measurement errors, but also on the properties of the source galaxies (namely, size, magnitude and spectral energy distribution). We are then able to compute the amplitude of the systematics power spectrum and its scaling with redshift, while we propose a multi-Gaussian expansion to model in a non-parametric way its angular scale dependence. Our method allows us to self-consistently propagate the systematics uncertainties to the finally observed shear power spectrum, thus allowing us to quantify the departures from the actual spectrum. We show that even a modest level of systematics can induce non-negligible deviations, thus leading to a significant bias on the recovered cosmological parameters.