Impact of spatial curvature on forecast constraints from standard and differential redshift drift measurements

The redshift drift of objects following the cosmological expansion is a unique model-independent probe of background cosmology, detectable by astrophysical facilities presently under construction. Previous forecasts for such measurements assume flat universes. We explore the impact of relaxing this assumption on the constraining power of the redshift drift, focusing on the two most promising routes for its measurement: the SKA at low redshifts, and the Golden Sample for the ELT's ANDES spectrograph at higher redshifts. We also discuss the cosmological sensitivity of possible differential redshift drift measurements, both on their own and, for the specific case of the Golden Sample, in combination with the standard method. Overall, we find that the sensitivity of the redshift drift to curvature is comparable to that of matter (especially at low redshifts) and higher than the sensitivity to the dark energy equation of state. We also show that the sensitivity of redshift drift measurements to these cosmological parameters is asymmetric with respect to the curvature parameter, being different for open and closed universes with the same absolute value of the curvature parameter $\Omega_k$.