Complementarity of the redshift drift

We derive some basic equations related to the redshift drift, and we show how some dark energy (DE) properties can be retrieved from it. We consider, in particular, three kinds of DE models which exhibit a characteristic signature in their redshift drift while no such signature would be present in their luminosity-distances: a sudden change of the equation of state parameter w(DE) at low redshifts, oscillating DE, and finally an equation of state with spikes at low redshifts. Accurate redshift-drift measurements would provide interesting complementary probes for some of these models and for models with varying gravitational coupling. While the redshift drift would efficiently constrain models with a spike at z similar to 1, the signature of the redshift drift for models with large variations at very low redshifts z < 0.1 would be unobservable, allowing a large arbitrariness in the present expansion of the Universe.