Influence of the local Universe on weak gravitational lensing surveys
  Observations of the large-scale structure (LSS) implicitly assume an ideal
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 large-scale structure observables
conditional on a property of the large-scale structure 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 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 be
approximately 4 percent. 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 $\Omega_m$ and $\sigma_8$ are
underestimated by a few percent. Thus, this effect will be important when
analysing data from future surveys such as Euclid, which aim at the
percent-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.
