Studying the precision of ray tracing techniques with Szekeres models

Abstract

The simplest standard ray tracing scheme employing the Born and Limber approximations and neglecting lens-lens coupling is used for computing the convergence along individual rays in mock N-body data based on Szekeres swiss cheese and onion models. The results are compared with the exact convergence computed using the exact Szekeres metric combined with the Sachs formalism. A comparison is also made with an extension of the simple ray tracing scheme which includes the Doppler convergence. The exact convergence is reproduced very precisely as the sum of the gravitational and Doppler convergences along rays in Lemaitre-Tolman-Bondi models. This is not the case when the models are based on non-symmetric Szekeres models. For such models, there is a significant deviation between the exact and ray traced paths and hence also the corresponding convergences.Comment: 28 pages, 16 captioned figures. Accepted for publication in Physical Review D. v2: Typos corrected (in appendix B and figure 6) + 2 references added. Results and conclusions unchanged. v3: Errors in section VI A and appendix C 2 corrected. Results in section VI A change

Light propagation in Swiss-cheese models of random close-packed Szekeres structures: Effects of anisotropy and comparisons with perturbative results

“…Results based on Swiss cheese models with LTB structures should be in line with perturbation theory; it has been shown with direct comparisons that perturbation theory based on (semi-)nonlinear LTB density fields and the corresponding exact velocity fields reproduces exact light propagation in LTB models very well [27,28] (see also [16,[29][30][31][32] for the relation between LTB models and perturbation theory). An important factor for the impressive reproductions of light propagation in LTB models with perturbation theory in [27,28] is the spherical symmetry of the LTB models; the reproduction is inhibited for anisotropic Szekeres structures because the method employed for obtaining velocity fields leads to artificial non-vanishing peculiar velocity fields outside non-spherically symmetric structures. That is, the method leads to non-vanishing peculiar velocity fields in regions where the exact anisotropic Szekeres models have reduced to FLRW models and hence should not give rise to peculiar velocity fields.…”

“…It is in this respect notable that anisotropic Szekeres models exhibit structure formation that deviates significantly from both that of the underlying LTB models and from predictions of perturbation theory [34][35][36][37][38]. In addition, it is very clear from figure 7a in [28] that light propagation is significantly affected by anisotropy; in that figure, it is seen that an initially radial light ray following an exact geodesic of an anisotropic Szekeres model moves through a significantly different density field than a light ray traced simply by using the Born approximation. Such a result is not possible for light rays in LTB models since the spherical symmetry dictates that an initially radial light ray remains so.…”

“…[62] for details). In particular, | det D a b | describes the angular diameter distance along the light ray when initial conditions are set appropriately (see [28] for initial conditions in the case of Szekeres models). The angular diameter distance along an individual light ray is therefore obtained by solving the transport equation simultaneously with the geodesic equations and the equations of parallel transport of E µ 1 , E µ 2 along the given null-geodesic.…”

Physical geometry of the quasispherical Szekeres models

“…But it fits particularly well with a model with a radially oscillating density, following the same series of r intervals. These kinds of models, called "Onion" models by some [24,42], are compatible with Sussman's prescription of periodic local homogeneity (PLH) [64].…”

Perturbatively constructed cosmological model with periodically distributed dust inhomogeneities

“…Among exact solutions to the Einstein field equa-tions, models considered in this context are the Lemaître-Tolman models [16,17,18] and their generalization, the Szekeres models [19,20,21,22]. These models are studied with matter distributed not only in a single halo cloud but also in various different ways, for example, in onion-like configurations [23,24,25] or in layers of walls [26,27]. Results of these studies can be compared with N-body relativistic simulations in a weak field approximation [22,24,25,28,29].…”