Redshift drift in radially inhomogeneous Lemaître-Tolman-Bondi spacetimes

Abstract

We provide a formula for estimating the redshift and its secular change (redshift drift) in Lema\^{\i}tre-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 ($\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$) model. We show that the redshift drift for these degenerate LTB models is typically different from that predicted in the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ 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 us to reduce the degrees of freedom of spherically symmetric models and to make them more predictive and thus falsifiable.