Cosmographic analysis of redshift drift

Redshift drift is the phenomenon whereby the observed redshift between an emitter and observer comoving with the Hubble flow in an expanding FLRW universe will slowly evolve—on a timescale comparable to the Hubble time. There are nevertheless serious astrometric proposals for actually observing this effect. We shall however pursue a more abstract theoretical goal, and perform a general cosmographic analysis of this effect, eschewing (for now) dynamical considerations in favour of purely kinematic symmetry considerations and Taylor series expansions based on FLRW spacetimes. We shall develop various exact results and series expansions for the redshift drift (and its derivatives) in terms of the present day Hubble, deceleration, jerk, snap, crackle, and pop parameters, as well as the present day redshift of the source. In particular, potential observation of this redshift drift effect is intimately related to the universe exhibiting a nonzero deceleration parameter.