Is Webb or any near-future telescopes like ELT capable of observing redshift changes to confirm General Relativity?

Question

The (Davis and Lineweaver (2003)) "Expanding Confusion" paper states that "the expected change in redshift due to cosmological acceleration or deceleration is only ∆z ∼ 10^(−8) over 100 years. Current Keck/HIRES spectra with iodine cell reference wavelengths can measure quasar absorption line redshifts to an accuracy of ∆z ∼ 10^(−5) (Outram et al., 1999). Thus, this observational test must wait for future technology."

Has JWST achieved or will ELT, etc. achieve this soon? And will this confirm the event horizon, particle horizon, and past light cone proper distances in their distance vs time graphs shown here and in Figure 1 in the paper?

Answer 1

The effect whereby, as the universe expands, the redshift of an object changes with time is known as redshift drift.

A galaxy at a fixed co-moving distance will have a redshift that changes with time and may prove to be valuable probes of cosmological models (e.g. Meli�� 2016).

An expression for the first order redshift drift is $$\frac{dz}{dt_0}= (1+z)H_0 - H(z),$$ where $H_0$ is the current Hubble parameter at time $t_0$ and $H(z)$ is the value of the Hubble parameter at an epoch corresponding to a redshift $z$.

The effect is small and depends on the exact cosmological parameters, which determine how the Hubble parameter changes with time. The rate of change of redshift is expected to be of order 10 cm/s/yr, with the difference between different cosmological models being smaller than this. The effect has not yet been probed with any useful level of sensitivity. The best I can find are measurements of galaxy redshifts on decadal timescales giving precisions more than 100 times too big to yield a detection (Darling 2012).

It is however a planned programme for the E-ELT telescope and the Square Kilometre Array, which may be able to measure redshift drift over 10-year periods, using large ensembles of galaxies and quasars at similar redshifts (e.g., Bolejko et al. 2019).