Parameterizing scalar-tensor theories for cosmological probes

We study the evolution of density perturbations for a class of f(R) models which closely mimic Lambda CDM 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 gamma in terms of M, and use our result to reconstruct the linear matter power spectrum. We find that the power spectrum at z similar to 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 gamma prescription in order to study structure formation for this class of models. Since gamma 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.