Influence of the local Universe on weak gravitational lensing surveys

Observations of the large-scale structure (LSS) implicitly assume an ideal Friedmann-Lemaitre-Robertson-Walker (FLRW) observer with the ambient structure having no influence on the observer. However, due to correlations in the LSS, cosmological observables are dependent on the position of an observer. We investigate this influence in full generality for a weakly non-Gaussian random field, for which we derive expressions for angular spectra of LSS observables conditional on a property of the LSS that is typical for the observer’s location. As an application, we then apply to the formalism to angular spectra of the weak gravitational lensing effect and provide numerical estimates for the resulting change on the spectra using linear structure formation. For angular weak lensing spectra, we find the effect to be of order of a few per cent, for instance we estimate for an overdensity of δ = 0.5 and multipoles up to ℓ = 100 the change in the weak lensing spectra to be approximately 4 per cent. We show that without accounting for correlation between the density at observer’s location and the weak gravitational lensing spectra, the values of the parameters Ωm and σ8 are underestimated by a few per cent. Thus, this effect will be important when analysing data from future surveys such as Euclid, which aim at the per cent-level precision. The effect is difficult to capture in simulations, as estimates of the number of numerical simulations necessary to quantify the effect are high