Observational constraints on viable f(R) parametrizations with geometrical and dynamical probes

Abstract

We demonstrate that a wide range of viable f(R) parametrizations (including the Hu and Sawicki and the Starobinsky models) can be expressed as perturbations deviating from the ΛCDM Lagrangian. We constrain the deviation parameter b using a combination of geometrical and dynamical observational probes. In particular, we perform a joint likelihood analysis of the recent type Ia supernova data, the cosmic microwave background shift parameters, the baryonic acoustic oscillations and the growth rate data provided by the various galaxy surveys. This analysis provides constraints for the following parameters: the matter density Ωm0, the deviation from ΛCDM parameter b and the growth index γ(z). We parametrize the growth index γ(z) in three manners (constant, Taylor expansion around z=0, and Taylor expansion around the scale factor). We point out the numerical difficulty for solving the generalized f(R) Friedmann equation at high redshifts due to the stiffness of the resulting ordinary differential equation. We resolve this problem by constructing an efficient analytical perturbative method in the deviation parameter b. We demonstrate that this method is highly accurate, by comparing the resulting analytical expressions for the Hubble parameter with the numerical solutions at low and intermediate redshifts. Surprisingly, despite its perturbative nature, the accuracy of the method persists even for values of b that are of O(1). © 2013 American Physical Society.