Cosmography and the redshift drift in Palatini f(R) theories

We present an application to cosmological models in f(R) theories within the Palatini formalism of a method that combines cosmography and the explicit form of the field equations in the calculation of the redshift drift. The method yields a sequence of constraint equations which lead to limits on the parameter space of a given f(R)-model. Two particular families of f(R)-cosmologies capable of describing the current dynamics of the universe are explored here: (i) power law theories of the type f(R)=R-β/Rn, and (ii) theories of the form f(R)=R+αlnR-β. The constraints on (n,β) and (α,β), respectively, limit the values to intervals that are narrower than the ones previously obtained. As a byproduct, we show that when applied to General Relativity, the method yields values of the kinematic parameters with much smaller errors that those obtained directly from observations.