Real-time cosmography with redshift derivatives

Abstract: The drift in the redshift of objects passively following the cosmological expansion has long been recognized as a key model-independent probe of cosmology. Here, we study the cosmological relevance of measurements of time or redshift derivatives of this drift, arguing that the combination of first and second redshift derivatives is a powerful test of the $\Lambda$CDM cosmological model. In particular, the latter can be obtained numerically from a set of measurements of the drift at different redshifts. We show that, in the low-redshift limit, a measurement of the derivative of the drift can provide a constraint on the jerk parameter, which is $j=1$ for flat $\Lambda$CDM, while generically $j\neq1$ for other models. We emphasize that such a measurement is well within the reach of the ELT-HIRES and SKA Phase 2 array surveys.