Local environmental dependence on weak-lensing shear statistics

TL;DR

The paper quantifies how the local cosmic environment affects weak-lensing shear statistics using relativistic N-body simulations with the 3D-RBT ray-bundle method. By analyzing PDFs, the shear angular power spectrum, and the shear bispectrum across halos and voids, it demonstrates that environmental bias on $\Omega_m$ is significant mainly below $z\approx 0.2$, and that the average impact on $f_{\rm NL}$ is minimal though rare observer locations could imply $f_{\rm NL}\sim 10$. The approach combines analytic predictions (Limber/Born for $C_{\ell}$ and bispectrum formalisms) with numerical WL maps, masking corrections, and MCMC constraints, providing a framework to propagate local-environment uncertainties into percent-level cosmological inferences. The results have implications for future wide-field surveys by highlighting the need to account for local environmental effects when interpreting WL shear statistics, particularly at low redshift and for non-Gaussianity studies.

Abstract

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.

Figures (14)

• Figure 1: Schematic diagram summarizing all the packages that we use for different purposes in this paper.
• Figure 2: WL shear PDFs with respect to redshift when observers are positioned in haloes with varying masses (Mass I: halo mass $<$$10^{12.5}$$\mathrm{M}_\odot$$h^{-1}$; Mass II: $10^{12.5}$$\mathrm{M}_\odot$$h^{-1}$$<$ halo mass $<$$10^{13.5}$$\mathrm{M}_\odot$$h^{-1}$; Mass III: $10^{13.5}$$\mathrm{M}_\odot$$h^{-1}$$<$ halo mass $<$$10^{14.5}$$\mathrm{M}_\odot$$h^{-1}$). Markers in this context represent mean PDFs, whereas error bars of varying colours display data indicating 68% deviation from the mean shear value within each mass range. The gray-shaded regions indicate the deviation band if the observer is randomly located within the simulation box.
• Figure 3: Changes in WL shear PDFs as based on redshift when observers were positioned in voids having different radii (Radius I: 10-20 Mpc/$h$; Radius II: 21-30 Mpc/$h$; Radius III: 31-40 Mpc/$h$). Markers in this context represent mean PDFs, whereas error bars of varying colours display data indicating 68% deviation from the mean shear value within each radius range. The gray-shaded regions indicate the deviation band if the observer is randomly located within the simulation box.
• Figure 4: Analysis of the shear angular power spectrum with respect to redshift for observers residing in haloes of varying masses. In this context, markers are used to represent mean values, while error bars of varying colours are used to display the data around the mean values for separate redshifts within each mass range. The gray-shaded regions indicate the deviation band if the observer is randomly located within the simulation box. The orange-shaded regions indicate the expected deviation band based on the shot noise contribution to the WL shear angular power spectrum.
• Figure 5: Analysis of the shear angular power spectrum with respect to redshift for observers residing in voids of varying radii. In this context, markers are used to represent mean values, while error bars of varying colours are used to display the data around the mean values for separate redshifts within each radius range. The gray-shaded regions indicate the deviation band if the observer is randomly located within the simulation box. The orange-shaded regions indicate the expected deviation band based on the shot noise contribution to the WL shear angular power spectrum.