Complete super-sample lensing covariance in the response approach

Alexandre Barreira, Elisabeth Krause, Fabian Schmidt

Research output: Contribution to journalArticlepeer-review

31 Scopus citations


We derive the complete super-sample covariance (SSC) of the matter and weak lensing convergence power spectra using the power spectrum response formalism to accurately describe the coupling of super- to sub-survey modes. The SSC term is completely characterized by the survey window function, the nonlinear matter power spectrum and the full first-order nonlinear power spectrum response function, which describes the response to super-survey density and tidal field perturbations. Generalized separate universe simulations can efficiently measure these responses in the nonlinear regime of structure formation, which is necessary for lensing applications. We derive the lensing SSC formulae for two cases: one under the Limber and flat-sky approximations, and a more general one that goes beyond the Limber approximation in the super-survey mode and is valid for curved sky applications. Quantitatively, we find that for sky fractions fsky 0.3 and a single source redshift at zS=1, the use of the flat-sky and Limber approximation underestimates the total SSC contribution by 10%. The contribution from super-survey tidal fields to the lensing SSC, which has not been included in cosmological analyses so far, is shown to represent about 5% of the total lensing covariance on multipoles ℓ1,ℓ2 300. The SSC is the dominant off-diagonal contribution to the total lensing covariance, making it appropriate to include these tidal terms and beyond flat-sky/Limber corrections in cosmic shear analyses.

Original languageEnglish (US)
Article number015
JournalJournal of Cosmology and Astroparticle Physics
Issue number6
StatePublished - Jun 11 2018
Externally publishedYes


  • cosmological parameters from LSS
  • dark energy experiments
  • gravitational lensing
  • weak gravitational lensing

ASJC Scopus subject areas

  • Astronomy and Astrophysics


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