Large-scale weak lensing convergence in nonlinear general relativity

Abstract

In this work we investigate the weak lensing convergence using an end-to-end nonlinear general relativistic framework. Combining numerical relativity simulations of large-scale structure formation with general relativistic ray-tracing, we compare our nonlinear calculation to the expectation based on perturbation theory for a set of 20 synthetic observers. We focus on large angular scales $\ell < 100$ across a broad range of redshifts with $0.05<z<3$. We confirm the importance of Doppler lensing for redshifts below $z\sim$0.6, as predicted by previous works. On average across our observers, linear perturbation theory predicts the nonlinear convergence to within 3-30% across all redshifts and angular scales we study. In general, we find smaller angular scales are better matched by linear theory than larger angular scales. While we cannot definitively identify the source of the discrepancy, for our particular study of redshift slices on observers' light cones the differences are mostly below the level of cosmic variance.

Figures (15)

• Figure 1: Full sky maps of the nonlinear convergence (left columns), the linearised convergence from the density field (center columns), and the Doppler lensing (right columns) for three slices with mean redshifts $\langle z \rangle=0.5$ (top row) and $\langle z \rangle=1.0$ (bottom row). These maps are for one single observer in the simulation with $N=256$. Note the colorbar limits differ for the bottom right panel since the Doppler lensing signal is much smaller at higher redshifts.
• Figure 2: Standard deviation of fluctuations in the lensing convergence across the sky as a function of mean redshift. We show the nonlinear signal, $\kappa$ (blue solid curve), as well as the linearised contributions $\kappa_\delta$ (green dashed curve), $\kappa_v$ (red dotted curve), $\kappa_{\rm SW}$ (orange dot-dashed curve), and $\kappa_{\rm ISW}$ (magenta dashed curve). The difference between the nonlinear convergence and all of the combined linearised contributions is shown by a thin black solid curve. Each line represents the standard deviation across the sky averaged over 20 observers in the $N=256$ simulation. Shaded regions around each curve show the full range of variance across all observers.
• Figure 3: Angular power spectra (averaged over 20 observers) of the relativistic convergence $\kappa$ (solid curves), the density convergence $\kappa_\delta$ (dashed curves), and the Doppler lensing $\kappa_v$ (dotted curves) as a function of angular scale, $\ell$, for two slices with mean redshift $\langle z \rangle = 0.5$ (top) and 1.0 (bottom). The shaded regions show the range within which all 20 observers' power spectra fall.
• Figure 4: Angular power spectra of the nonlinear convergence (blue solid curves), linearised convergence from the density (green dashed curves) as well as all known relativistic contributions. The Doppler lensing is shown by the red dashed curves, the SW is the orange dot-dashed curves, and the ISW contribution is the magenta dashed curves. Top panels show the power spectrum averaged over all 20 observers with shaded regions showing the range of minimum to maximum over all observers. Bottom panels show the absolute difference in the power spectra when comparing $\kappa$ and $\kappa_\delta$ (dotted curves), $\kappa$ and $\kappa_\delta + \kappa_v$ (dashed curves), and $\kappa$ and $\kappa_\delta + \kappa_v + \kappa_{\rm SW} + \kappa_{\rm ISW}$ (solid curves). In the bottom panel, thick curves are the mean over 20 observers and thinner curves show individual observers, with red dot-dashed curves showing the cosmic variance limit as a function of $\ell$. Left panels show slices with $\langle z \rangle = 0.5$ and right panels show $\langle z \rangle = 1.0$.
• Figure 5: Redshift evolution of the relative difference in power spectra between nonlinear and linearised convergence. Solid curves show the difference when only including $\kappa_\delta$, dashed curves show the difference when including $\kappa_\delta + \kappa_v$, and dotted curves (left panel only) show the difference when including the SW and ISW contributions. Dot-dashed horizontal lines show the cosmic variance limit for the $\ell$ of the same colour. Left panel shows $\ell<10$ and right panel shows $\ell\geq10$.