Cosmography and the redshift drift in Palatini $$f({{\mathcal {R}}})$$ f(R) theories

Abstract

Abstract We present an application to cosmological models in $$f({{\mathcal {R}}})$$ 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 $$f({{\mathcal {R}}})$$ f(R) -model. Two particular families of $$f(\mathcal{R})$$ f(R) -cosmologies capable of describing the current dynamics of the universe are explored here: (i) power law theories of the type $$f({{\mathcal {R}}})={{\mathcal {R}}}-\beta /{{\mathcal {R}}}^n$$ f(R)=R-β/Rn , and (ii) theories of the form $$f({{\mathcal {R}}})={{\mathcal {R}}}+\alpha \ln {{{\mathcal {R}}}} -\beta $$ f(R)=R+αlnR-β . The constraints on $$(n,\beta )$$ (n,β) and $$(\alpha ,\beta )$$ (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.