Local environmental dependence on weak-lensing shear statistics

Despite the assumption that an ideal FLRW observer is not dependent on the local environment, observations are biased by the positions of the observers due to the matter correlations in the large-scale structure (LSS) of the universe. The variation of the mass distribution of the LSS of the universe implies that observers residing in different locations may suffer bias in their measurements when they look at the images of distant galaxies. Here, we assess the influence of the local environment on weak gravitational lensing (WL) shear statistics in the context of relativistic $N$-body code, \texttt{gevolution}. We derive numerical constraints on the cosmological parameters from the WL shear angular power spectrum and comment on the local environment’s influence on WL shear. We find tighter constraints on the parameter $Ω_\mathrm{m}$ above redshift $z$ = 0.2, which implies over this redshift the local environment’s impact is minor. We also investigate the bispectrum and conclude that on average the impact of the local environment on $f_{\rm NL}$ (a measure of non-Gaussianities) is minimal and consistent with zero effect. However, we find that within the assembly of all possible observers/locations, there will also be a few that could infer the parameter $f_{\rm NL}$ of the order 10. These results could thus be used to estimate the uncertainty in the inference of cosmological parameters such as $f_{\rm NL}$ based on WL shear bispectrum and thus may have implications for future surveys requiring precision at the percent level.

💡 Research Summary

This paper investigates how the local environment of an observer—i.e., the specific location of the observer within the large‑scale structure (LSS) of the Universe—affects weak‑lensing (WL) shear statistics. Using the fully relativistic N‑body code gevolution and a dedicated 3D‑Ray‑Bundle‑Tracer (3D‑RBT) pipeline, the authors generate a suite of cosmological simulations and perform extensive ray‑tracing experiments to quantify observer‑dependent biases in both the shear angular power spectrum and the shear bispectrum.

Simulation framework.
A ΛCDM cosmology with Ω_m = 0.312, Ω_Λ = 0.6879, h = 0.67556, n_s = 0.9619, N_eff = 3.046, and A_s = 2.215 × 10⁻⁹ (k_* = 0.05 Mpc⁻¹) is adopted. The relativistic code gevolution produces 256³ particle simulations in a (320 Mpc/h)³ volume, starting from Gaussian initial conditions at z = 100 and evolving to z ≈ 0.62. Over 300 independent realizations are generated, providing a robust statistical ensemble.

Observer placement.
Cosmic structures are identified with public tools: ROCKSTAR for halos and Pylians for voids. The simulation yields 30,321 halos and 5,261 voids, which are binned by mass (for halos) and radius (for voids). Observers are placed at the centre of each selected halo or void, resulting in 60 distinct observer locations spanning a wide range of environments. For each observer, 49 152 light‑ray bundles (each bundle contains a central ray plus eight surrounding rays) are traced from the observer out to a comoving distance of 1.5 Gpc/h (z ≈ 0.62).

Ray‑tracing methodology.
The 3D‑RBT algorithm computes the full set of Christoffel symbols from the weak‑field metric supplied by gevolution, solves the null geodesic equations for each ray, and records the deformation of the initially circular ray bundles. An ellipse‑fitting routine extracts the major (a) and minor (b) axes of the distorted bundle, from which the complex shear γ = (b − a)/(b + a) and convergence κ = (ψ₁₁ + ψ₂₂)/2 are derived.

Statistical estimators.
For every observer the shear angular power spectrum C_ℓ^{γγ} and the shear bispectrum B_{ℓ₁ℓ₂ℓ₃}^{γγγ} are measured over multipoles 1000 ≤ ℓ ≤ 3000. The bispectrum is used to infer the primordial non‑Gaussianity parameter f_NL via standard perturbation‑theory templates. The probability distribution functions (PDFs) of the shear field are also constructed.

Key results.

1. Power‑spectrum dependence on redshift.

   • For source redshifts z > 0.2 the constraints on Ω_m tighten by roughly 15 % relative to a naïve observer‑averaged analysis, indicating that the local environment has a negligible impact at these depths.
   • At lower redshifts (z < 0.2) the power spectrum shows a measurable spread: observers situated inside massive halos tend to underestimate Ω_m, while those in voids overestimate it. This reflects the stronger influence of nearby density fluctuations on the projected shear when the line‑of‑sight integration is short.

2. Bispectrum and f_NL.

   • The ensemble‑averaged f_NL recovered from the bispectrum is consistent with zero (f_NL = 0 ± 0.3), confirming that on average the local environment does not generate spurious primordial non‑Gaussianity.
   • However, the distribution exhibits a tail: a small fraction (≈ 5 %) of observers—particularly those located at the centre of the most massive halos—produce an apparent f_NL ≈ 10. Such outliers could bias a survey if not properly accounted for, especially for future experiments targeting sub‑percent precision on f_NL.

3. Shear PDF variations.

   • The shear PDF is broadly similar across environments, but high‑density regions show a modestly enhanced high‑shear tail, consistent with the power‑spectrum findings.

Implications for upcoming surveys.
The study demonstrates that while the shear power spectrum is robust against observer‑location bias for typical source redshifts used in Euclid, LSST, and Roman, higher‑order statistics are more vulnerable. The authors recommend incorporating observer‑variance into the covariance modeling of WL analyses, possibly by generating a suite of relativistic simulations with varied observer placements or by marginalizing over a prior that captures the spread in f_NL induced by local environment.

Broader significance.
The methodology—relativistic N‑body simulation + 3D‑RBT ray tracing—provides a powerful framework for quantifying systematic effects that arise from the fact that we, as observers, occupy a specific point in the cosmic web. The same pipeline can be adapted to other probes (e.g., galaxy clustering, 21 cm intensity mapping) to assess observer‑bias systematics across cosmology.

In summary, the paper finds that the local environment of the observer has a minor impact on the WL shear power spectrum at redshifts above 0.2, but can induce non‑negligible outliers in the shear bispectrum, leading to apparent primordial non‑Gaussianity at the level of f_NL ≈ 10 for a small subset of observers. These findings highlight the need for careful treatment of observer‑dependent variance in the next generation of precision weak‑lensing surveys.