General relativistic corrections to the weak lensing convergence power spectrum

We compute the weak lensing convergence power spectrum, $C_{\ell }^{\kappa \kappa }$, in a dust-filled universe using fully nonlinear general relativistic simulations. The spectrum is then compared to more standard, approximate calculations by computing the Bardeen (Newtonian) potentials in linearized gravity and partially utilizing the Born approximation. We find corrections to the angular power spectrum amplitude of order ten percent at very large angular scales, $\ell \sim 2–3$, and percent-level corrections at intermediate angular scales of $\ell \sim 20–30$.

Figure 1

Observed skies: top left is a sky generated using approximate theory [Eq. (10)], top right a relativistic sky [Eq. (9)], and bottom the difference between the two. These skies are generated using a Healpix resolution of $\mathrm{Nside}=32$, and all maps have had the angular monopole and dipole contributions removed.

Figure 2

Power spectra of the simulated skies shown in Fig. 1. The brown (solid) curve depicts results from a fully relativistic run, teal (dashed) from approximate theory, dark purple (dotted) the average power spectrum of the difference map, and light purple (dot-dashed) a direct subtraction of the GR and approximate power spectra.

Figure 3

Shown are averages of 20 power spectra obtained from independent simulations. The brown (solid) curve shows the fully relativistic power spectrum, and teal (dashed) the approximate spectrum. The dark purple (dotted) curve is the average power spectrum of the difference maps, and the light purple (dot-dashed) power spectrum the average of a direct subtraction of the GR and approximate power spectra.