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

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.