Luminosity distance and redshift in the Szekeres inhomogeneous cosmological models

Abstract

The Szekeres inhomogeneous models can be used to model the true lumpy\nuniverse that we observe. This family of exact solutions to Einstein's\nequations was originally derived with a general metric that has no symmetries.\nIn this work, we develop and use a framework to integrate the angular diameter\nand luminosity distances in the general Szekeres models. We use the affine null\ngeodesic equations in order to derive a set of first-order ordinary\ndifferential equations that can be integrated numerically to calculate the\npartial derivatives of the null vector components. These equations allow the\nintegration in all generality of the distances in the Szekeres models and some\nexamples are given. The redshift is determined from simultaneous integration of\nthe null geodesic equations. This work does not assume spherical or axial\nsymmetry, and the results will be useful for comparisons of the general\nSzekeres inhomogeneous models to current and future cosmological data.\n