# A fitting formula for the non-Gaussian contribution to the lensing power spectrum covariance

J. Pielorz, J. R\"odiger, I. Tereno and P. Schneider

Arxiv ID: 0907.1524•Last updated: 11/7/2022

Weak gravitational lensing is one of the most promising tools to investigate
the equation-of-state of dark energy. In order to obtain reliable parameter
estimations for current and future experiments, a good theoretical
understanding of dark matter clustering is essential. Of particular interest is
the statistical precision to which weak lensing observables, such as cosmic
shear correlation functions, can be determined. We construct a fitting formula
for the non-Gaussian part of the covariance of the lensing power spectrum. The
Gaussian contribution to the covariance, which is proportional to the lensing
power spectrum squared, and optionally shape noise can be included easily by
adding their contributions. Starting from a canonical estimator for the
dimensionless lensing power spectrum, we model first the covariance in the halo
model approach including all four halo terms for one fiducial cosmology and
then fit two polynomials to the expression found. On large scales, we use a
first-order polynomial in the wave-numbers and dimensionless power spectra that
goes asymptotically towards $1.1 C_{pt}$ for $\ell \to 0$, i.e., the result for
the non-Gaussian part of the covariance using tree-level perturbation theory.
On the other hand, for small scales we employ a second-order polynomial in the
dimensionless power spectra for the fit. We obtain a fitting formula for the
non-Gaussian contribution of the convergence power spectrum covariance that is
accurate to 10% for the off-diagonal elements, and to 5% for the diagonal
elements, in the range $50 \lesssim \ell \lesssim 5000$ and can be used for
single source redshifts $z_{s} \in [0.5,2.0]$ in WMAP5-like cosmologies.

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