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

TL;DR

This paper develops a fitting formula for the non-Gaussian part of the lensing power spectrum covariance, improving the accuracy of statistical error estimates in weak lensing studies for dark energy research.

Contribution

It introduces a novel polynomial fitting formula for the non-Gaussian covariance, based on halo model calculations, applicable across a wide range of scales and redshifts.

Findings

Achieves 10% accuracy for off-diagonal covariance elements.

Achieves 5% accuracy for diagonal elements.

Applicable for scales 50 to 5000 and redshifts 0.5 to 2.0.

Abstract

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.