  The redshift drift of objects moving in the Hubble flow has been proposed as
a powerful model-independent probe of the underlying cosmology. A measurement
of the first and second order redshift derivatives appears to be well within
the reach of upcoming surveys using ELT-HIRES and the SKA Phase 2 array. Here
we show that an unambiguous prediction of the R_h=ct cosmology is zero drift at
all redshifts, contrasting sharply with all other models in which the expansion
rate is variable. For example, multi-year monitoring of sources at redshift z=5
with the ELT-HIRES is expected to show a velocity shift Delta v = -15 cm/s/yr
due to the redshift drift in Planck LCDM, while Delta v=0 cm/s/yr in R_h=ct.
With an anticipated ELT-HIRES measurement error of +/-5 cm/s/yr after 5 years,
these upcoming redshift drift measurements might therefore be able to
differentiate between R_h=ct and Planck LCDM at ~3 sigma, assuming that any
possible source evolution is well understood. Such a result would provide the
strongest evidence yet in favour of the R_h=ct cosmology. With a 20-year
baseline, these observations could favor one of these models over the other at
better than 5 sigma.
