# Influence of the local Universe on weak gravitational lensing surveys

## TL;DR

This paper investigates how the local large-scale structure around an observer influences weak gravitational lensing measurements, revealing a few percent effect that impacts parameter estimation in future high-precision surveys.

## Contribution

It derives a formalism for the influence of local universe structures on weak lensing spectra and provides numerical estimates showing a significant impact on cosmological parameters.

## Key findings

- Weak lensing spectra are affected by local structure at the few percent level.
- Neglecting local structure leads to underestimating parameters like Ω_m and σ_8.
- The effect is relevant for future surveys aiming at percent-level precision.

## Abstract

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.