Abstract
We study the evolution of density perturbations for a class of f(R) models which closely mimic ΛCDM background cosmology. Using the quasi-static approximation, and the fact that these models are equivalent to scalar-tensor gravity, we write the modified Friedmann and cosmological perturbation equations in terms of the mass M of the scalar field. Using the perturbation equations, we then derive an analytic expression for the growth parameter γ in terms of M, and use our result to reconstruct the linear matter power spectrum. We find that the power spectrum at z ∼ 0 is characterized by a tilt relative to its General Relativistic form, with increased power on small scales. We discuss how one has to modify the standard, constant γ prescription in order to study structure formation for this class of models. Since γ is now scale and time dependent, both the amplitude and transfer function associated with the linear matter power spectrum will be modified. We suggest a simple parameterization for the mass of the scalar field, which allows us to calculate the matter power spectrum for a broad class of f(R) models.
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