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

We demonstrate that a wide range of viable f(R) parameterizations (including the Hu & Sawicki and the Starobinsky models) can be expressed as perturbations deviating from the LCDM 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 Supernovae Type Ia 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 Omega_{m0}, the deviation from LCDM parameter b and the growth index gamma(z). We parametrize the growth index gamma(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) Friedman equation at high redshifts due to 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 of its perturbative nature, the accuracy of the method persists even for values of b that are of O(1).