The integrated three-point correlation function of cosmic shear

Feb 19, 2021
18 pages
Published in:
  • Mon.Not.Roy.Astron.Soc. 506 (2021) 2, 2780-2803
  • Published: Jul 23, 2021
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Abstract: (Oxford University Press)
We present the integrated three-point shear correlation function iζ_± – a higher order statistic of the cosmic shear field – which can be directly estimated in wide-area weak lensing surveys without measuring the full three-point shear correlation function, making this a practical and complementary tool to two-point statistics for weak lensing cosmology. We define it as the one-point aperture mass statistic M_ap measured at different locations on the shear field correlated with the corresponding local two-point shear correlation function ξ_±. Building upon existing work on the integrated bispectrum of the weak lensing convergence field, we present a theoretical framework for computing the integrated three-point function in real space for any projected field within the flat-sky approximation and apply it to cosmic shear. Using analytical formulae for the non-linear matter power spectrum and bispectrum, we model iζ_± and validate it on N-body simulations within the uncertainties expected from the sixth year cosmic shear data of the Dark Energy Survey. We also explore the Fisher information content of iζ_± and perform a joint analysis with ξ_± for two tomographic source redshift bins with realistic shape noise to analyse its power in constraining cosmological parameters. We find that the joint analysis of ξ_± and iζ_± has the potential to considerably improve parameter constraints from ξ_± alone, and can be particularly useful in improving the figure of merit of the dynamical dark energy equation of state parameters from cosmic shear data.
Note:
  • Accepted for publication in MNRAS; v2 matches the accepted manuscript; 18 pages + appendix
  • gravitational lensing: weak
  • methods: statistical
  • cosmological parameters
  • large-scale structure of Universe