Euclid preparation: XXVIII. Forecasts for ten different higher-order weak lensing statistics

Euclid Collaboration

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7 Scopus citations


Recent cosmic shear studies have shown that higher-order statistics (HOS) developed by independent teams now outperform standard two-point estimators in terms of statistical precision thanks to their sensitivity to the non-Gaussian features of large-scale structure. The aim of the Higher-Order Weak Lensing Statistics (HOWLS) project is to assess, compare, and combine the constraining power of ten different HOS on a common set of Euclid-like mocks, derived from N-body simulations. In this first paper of the HOWLS series, we computed the nontomographic (Ωm, σ 8) Fisher information for the one-point probability distribution function, peak counts, Minkowski functionals, Betti numbers, persistent homology Betti numbers and heatmap, and scattering transform coefficients, and we compare them to the shear and convergence two-point correlation functions in the absence of any systematic bias. We also include forecasts for three implementations of higher-order moments, but these cannot be robustly interpreted as the Gaussian likelihood assumption breaks down for these statistics. Taken individually, we find that each HOS outperforms the two-point statistics by a factor of around two in the precision of the forecasts with some variations across statistics and cosmological parameters. When combining all the HOS, this increases to a 4.5 times improvement, highlighting the immense potential of HOS for cosmic shear cosmological analyses with Euclid. The data used in this analysis are publicly released with the paper.

Original languageEnglish (US)
Article numberA120
JournalAstronomy and Astrophysics
StatePublished - Jul 1 2023

All Science Journal Classification (ASJC) codes

  • Astronomy and Astrophysics
  • Space and Planetary Science


  • Cosmological parameters
  • Gravitational lensing: weak
  • Large-scale structure of Universe
  • Methods: statistical
  • Surveys


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