Preparing for the Cosmic Shear Data Flood: Optimal Data Extraction and Simulation Requirements for Stage IV Dark Energy Experiments

Upcoming photometric lensing surveys will considerably tighten constraints on the neutrino mass and the dark energy equation of state. Nevertheless it remains an open question of how to optimally extract the information and how well the matter power spectrum must be known to obtain unbiased cosmological parameter estimates. By performing a Principal Component Analysis (PCA), we quantify the sensitivity of 3D cosmic shear and tomography with different binning strategies to different regions of the lensing kernel and matter power spectrum, and hence the background geometry and growth of structure in the Universe. We find that a large number of equally spaced tomographic bins in redshift can extract nearly all the cosmological information without the additional computational expense of 3D cosmic shear. Meanwhile a large fraction of the information comes from small poorly understood scales in the matter power spectrum, that can lead to biases on measurements of cosmological parameters. In light of this, we define and compute a cosmology-independent measure of the bias due to imperfect knowledge of the power spectrum. For a Euclid-like survey, we find that the power spectrum must be known to an accuracy of less than 1% on scales with k = 7 h /Mpc This requirement is not absolute since the bias depends on the magnitude of modelling errors, where they occur in k-z space, and the correlation between them, all of which are specific to any particular model. We therefore compute the bias in several of the most likely modelling scenarios and introduce a general formalism and public code, RequiSim, to compute the expected bias from any non-linear model.