Redshift Drift in LTB Void Universes

TL;DR

This paper investigates the redshift drift in LTB void universe models, demonstrating it is always negative for off-center sources and can be positive with significant inhomogeneity, offering a way to distinguish such models from dark energy scenarios.

Contribution

It provides a detailed analysis of redshift drift in LTB models, proving negativity for off-center sources and identifying conditions for positive drift due to large inhomogeneities.

Findings

Redshift drift is always negative for off-center sources in LTB void models.

Redshift drift can be positive with large inhomogeneity.

Observations of redshift drift can distinguish between LTB void models and dark energy models.

Abstract

We study the redshift drift, i.e., the time derivative of the cosmological redshift in the Lema\^itre-Tolman-Bondi (LTB) solution in which the observer is assumed to be located at the symmetry center. This solution has often been studied as an anti-Copernican universe model to explain the acceleration of cosmic volume expansion without introducing the concept of dark energy. One of decisive differences between LTB universe models and Copernican universe models with dark energy is believed to be the redshift drift. The redshift drift is negative in all known LTB universe models, whereas it is positive in the redshift domain $z \lesssim 2$ in Copernican models with dark energy. However, there have been no detailed studies on this subject. In the present paper, we prove that the redshift drift of an off-center source is always negative in the case of LTB void models. We also show that the redshift drift can be positive with an extremely large hump-type inhomogeneity. Our results suggest that we can determine whether we live near the center of a large void without dark energy by observing the redshift drift.