Methods for studying the accuracy of light propagation in N -body simulations
It is proposed to use exact, cosmologically relevant solutions to Einstein's equations to accurately quantify the precision of ray tracing techniques through Newtonian N-body simulations. As an initial example of such a study, the recipe in (Green & Wald, 2012) for going between N-body results and a perturbed FLRW metric in the Newtonian gauge is used to study light propagation through quasi-spherical Szekeres models. The study is conducted by deriving a set of ODEs giving an expression for the angular diameter distance in the Newtonian gauge metric. The accuracy of the results obtained from the ODEs is estimated by using the ODEs to determine the distance-redshift relation in mock N-body data based on quasi-spherical Szekeres models. The results are then compared to the exact relations. From this comparison it is seen that the obtained ODEs can accurately reproduce the distance-redshift relation along both radial and non-radial geodesics in spherically symmetric models. The reproduction of geodesics in non-symmetric Szekeres models is slightly less accurate, but still good. These results indicate that the employment of perturbed FLRW metrics for standard ray tracing techniques yields fairly accurate results, at least regarding distance-redshift relations. It is possible though, that this conclusion will be rendered invalid if other typical ray tracing approximations are included and if light is allowed to travel through several structures instead of just one.