1702.05301
Precision calculations of the cosmic shear power spectrum projection
Kilbinger, et al
Compute the spherical-sky WL power spectrum of the shear and convergence. Discuss various approximations, such as flat-sky, and first- and second-order Limber equations for the projection. Find that the impact of adopting these approximations are negligible when constraining cosmological parameters from current WL surveys. This is demonstrated using CFHTLenS. Find that the reported tension with Planck CMB temperature anisotropy results cannot be alleviated, in contrast to the recent claim made by Kitching et al (2016, version 1). For future large-scale surveys with unprecedented precision, show that the spherical second-order Limber approximation will provide sufficient accuracy. In this case, the cosmic-shear power spectrum is shown to be in agreement with the full projection at the sub-percent level for ell>3, with the corresponding errors an order of magnitude below comic variance for all ell. When computing the two-point shear correlation function, show that the flat-sky fast Hankel transformation results in errors below two percent compared to the full spherical transformation. In the spirit of reproducible research, the numerical implementation of all approximations and the full projection are publicly available within the package nicaea at www.cosmostat.org/software/nicaea.
Precision calculations of the cosmic shear power spectrum projection
Kilbinger, et al
Compute the spherical-sky WL power spectrum of the shear and convergence. Discuss various approximations, such as flat-sky, and first- and second-order Limber equations for the projection. Find that the impact of adopting these approximations are negligible when constraining cosmological parameters from current WL surveys. This is demonstrated using CFHTLenS. Find that the reported tension with Planck CMB temperature anisotropy results cannot be alleviated, in contrast to the recent claim made by Kitching et al (2016, version 1). For future large-scale surveys with unprecedented precision, show that the spherical second-order Limber approximation will provide sufficient accuracy. In this case, the cosmic-shear power spectrum is shown to be in agreement with the full projection at the sub-percent level for ell>3, with the corresponding errors an order of magnitude below comic variance for all ell. When computing the two-point shear correlation function, show that the flat-sky fast Hankel transformation results in errors below two percent compared to the full spherical transformation. In the spirit of reproducible research, the numerical implementation of all approximations and the full projection are publicly available within the package nicaea at www.cosmostat.org/software/nicaea.
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