Redshift drift in radially inhomogeneous Lema\^itre-Tolman-Bondi spacetimes

TL;DR

This paper derives a formula for redshift drift in Lemaître-Tolman-Bondi universes, compares it with standard cosmology, and discusses how it can distinguish between models despite similar Hubble diagrams.

Contribution

It introduces a new formula for redshift drift in LTB models and explores its potential to differentiate these models from standard cosmology.

Findings

Redshift drift differs in LTB models from standard $\\Lambda$CDM predictions.

Degenerate LTB models can mimic $\\Lambda$CDM Hubble diagrams but differ in redshift drift.

Redshift drift can serve as a falsifiable metric observable for spherically symmetric universes.

Abstract

We provide a formula for estimating the redshift and its secular change (redshift drift) in Lema\^itre-Tolman-Bondi (LTB) spherically symmetric universes. We compute the scaling of the redshift drift for LTB models that predict Hubble diagrams indistinguishable from those of the standard cosmological model, the flat $\Lambda$ Cold Dark Matter ($\Lambda$CDM) model. We show that the redshift drift for these degenerate LTB models is typically different from that predicted in the $\Lambda$CDM scenario. We also highlight and discuss some unconventional redshift-drift signals that arise in LTB universes and give them distinctive features compared to the standard model. We argue that the redshift drift is a metric observable that allows to reduce the degrees of freedom of spherically symmetric models and to make them more predictive and thus falsifiable.