The integrated angular bispectrum of weak lensing

Abstract

We investigate three-point statistics in weak lensing convergence, through the integrated angular bispectrum. It involves measuring the three-point function of harmonic multipoles of the lensing field by estimating how the angular power spectrum (two-point function) in patches is modulated by large scale modes. This approach avoids the complexity of estimating the very large number of possible bispectrum configurations. The integrated bispectrum mainly probes the squeezed limit of the bispectrum. Previous studies have compared measurements of the integrated bispectrum on the sphere against theoretical prediction, finding overall good consistency. It is crucial, to apply this statistic to data analysis and parameter estimation, to extract the covariance matrix. This requires applying the integrated bispectrum estimator to many thousands simulations, however the current implementation is too slow. Therefore, in this thesis, we investigate a new implementation, based on the so-called flat-sky approximation, in which the power spectrum in small patches of the spherical domain is computed via a tangent-plane projection.We investigate three-point statistics in weak lensing convergence, through the integrated angular bispectrum. It involves measuring the three-point function of harmonic multipoles of the lensing field by estimating how the angular power spectrum (two-point function) in patches is modulated by large scale modes. This approach avoids the complexity of estimating the very large number of possible bispectrum configurations. The integrated bispectrum mainly probes the squeezed limit of the bispectrum. Previous studies have compared measurements of the integrated bispectrum on the sphere against theoretical prediction, finding overall good consistency. It is crucial, to apply this statistic to data analysis and parameter estimation, to extract the covariance matrix. This requires applying the integrated bispectrum estimator to many thousands simulations, however the current implementation is too slow. Therefore, in this thesis, we investigate a new implementation, based on the so-called flat-sky approximation, in which the power spectrum in small patches of the spherical domain is computed via a tangent-plane projection