Preparing for the cosmic shear data flood: Optimal data extraction and simulation requirements for stage IV dark energy experiments

Abstract

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 ≤ 7h Mpc −1 . This requirement is not absolute since the bias depends on the magnitude of modeling 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 modeling scenarios and introduce a general formalism and public code, RequiSim, to compute the expected bias from any nonlinear model.

Rainbow cosmic shear: Optimization of tomographic bins

“…This is complementary to the conclusions of [13] who find that for a sufficiently large number of bins both an equal-number and equal-spaced configuration captures all the 3D information from the shear field, but that as the number of bins increased the equal-number case converges more slowly than the equal-spaced case. The reason why equally-spaced bins are optimal is two-fold: the bins are orthogonal, and the equal-spacing provides better redshift coverage for dark energy measurements.…”

“…The most widely used cosmic shear power spectrum formulation uses the Limber [10], flat-Universe [11] and equal-time [12] approximations, and creates bins in redshift known as 'tomographic' bins. This approach was generalised in [13] to a generalised spherical-transform that is defined as:…”

“…In principle each pixel in the self-organising map (or equivalently voxel in colour space) could be used as a distinct tomographic bin. In this approach, as shown by [13], the total 3D shear-field information would be fully captured. The utility of binning the data is therefore only one of computational nature and regularisation.…”

Nonparametric cosmology with cosmic shear

“…Meanwhile we refer to the information contained in these amplitudes and functions as the nonparametric information. This study directly builds off [20] where we found the precise scales and redshifts where cosmic shear is sensitive to the power spectrum and comoving distance.…”

“…We choose to use the shear two-point statistic. Even though this only accesses the Gaussian information of the shear field, a large body of work exists to provide rigorous requirements on systematics to ensure unbiased results [19][20][21].…”