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Observations of the large-scale structure (LSS) implicitly assume an idealFLRW observer with the ambient structure having no influence on the observer.However, due to correlations in the LSS, cosmological observables are dependenton the position of an observer. We investigate this influence in fullgenerality for a weakly non-Gaussian random field, for which we deriveexpressions for angular spectra of large-scale structure observablesconditional on a property of the large-scale structure that is typical for theobserver's location. As an application, we then apply to the formalism toangular spectra of the weak gravitational lensing effect and provide numericalestimates for the resulting change on the spectra using linear structureformation. For angular weak lensing spectra we find the effect to be of orderof a few percent, for instance we estimate for an overdensity of $\delta =0.5$and multipoles up to $\ell=100$ the change in the weak lensing spectra to beapproximately 4 percent. We show that without accounting for correlationbetween the density at observer's location and the weak gravitational lensingspectra, the values of the parameters $\Omega_m$ and $\sigma_8$ areunderestimated by a few percent. Thus, this effect will be important whenanalysing data from future surveys such as Euclid, which aim at thepercent-level precision. The effect is difficult to capture in simulations, asestimates of the number of numerical simulations necessary to quantify theeffect are high.

Influence of the local Universe on weak gravitational lensing surveys