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

Abstract

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

7 pages, 2 figures