Martin Kilbinger, 2010, arXiv:1004.3493

Description

We provide fitting formulae for the reduced-shear power-spectrum correction which is third-order in the lensing potential. This correction reaches up to 10% of the total lensing spectrum. Higher-order correction terms are one order of magnitude below the third-order term. The correction involves an integral over the matter bispectrum. We fit this integral with a combination of power-law functions and polynomials. We also fit the derivatives with respect to cosmological parameters. A Taylor-expansion around a fiducial (WMAP7) model provides accurate reduced-shear corrections within a region in parameter space containing the WMAP7 68% error elllipsoid.

Our fits are accurate to 1% for l<10^{4}, and to 2% for l<2·10^{5}, which reduces the bias by
a factor of four compared to the case of no correction. This matches the precision lensing power spectrum predictions
of recent N-body simulations.

The code

Download an example code which includes the fitting matrices.
Use 'make' to compile the code. To use the code, you have to fill in F^{mn}(a) (eq. 10 from the paper) which involves the lensing efficiency, comoving distances and the redshift distribution(s).

The reduced-shear corrections are also implemented in the cosmology and lensing package 'nicaea'. This code provides all necessary functions to produce lensing observables (shear power spectrum and real-space second-order functions). The cosmology and redshift distributions are set via parameter files.

The author

Martin Kilbinger (martin.kilbinger@cea.fr)

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Last updated 20 April 2010.