Exact inhomogeneous models and the drift of light rays induced by nonsymmetric flow of the cosmic medium

TL;DR

This paper investigates how light rays drift across the sky in inhomogeneous cosmological models, revealing measurable effects that distinguish these models from standard homogeneous models, and discusses conditions affecting this drift.

Contribution

It provides an exact analysis of light ray drift in inhomogeneous models, correcting misconceptions and linking the effect to shear and metric properties.

Findings

Galaxies can drift up to 10^{-6} arc seconds per year in certain models

The drift effect is zero in FLRW models, indicating inhomogeneity

Zero shear is necessary for zero drift in Szekeres models

Abstract

After introducing the Szekeres and Lema\^{\i}tre--Tolman cosmological models, the real-time cosmology program is briefly mentioned. Then, a few widespread misconceptions about the cosmological models are pointed out and corrected. Investigation of null geodesic equations in the Szekeres models shows that observers in favourable positions would see galaxies drift across the sky at a rate of up to $10^{-6}$ arc seconds per year. Such a drift would be possible to measure using devices that are under construction; the required time of monitoring would be $\approx10$ years. This effect is zero in the FLRW models, so it provides a measure of inhomogeneity of the Universe. In the Szekeres models, the condition for zero drift is zero shear. But in the shearfree normal models, the condition for zero drift is that, in the comoving coordinates, the time dependence of the metric completely factors out.