Parametrizing growth in dark energy and modified gravity models

Abstract

It is well known that an extremely accurate parametrization of the growth function of matter density perturbations in ACDM cosmology, with errors below 0.25%, is given by f(a) = Ω^(γ)_(m)(a) with γ ≃ 0.55. In this work, we show that a simple modification of this expression also provides a good description of growth in modified gravity theories. We consider the model-independent approach to modified gravity in terms of an effective Newton constant written as μ(a, k) = G_(eff)/G and show that f(a) = β(a) Ω^(γ)_(m)(a) provides fits to the numerical solutions with similar accuracy to that of ACDM. In the time-independent case with μ ¼ μðkÞ, simple analytic expressions for βðμÞ and γðμÞ are presented. In the time-dependent (but scaleindependent) case μ = μ(a), we show that β(a) has the same time dependence as μ(a). As an example, explicit formulas are provided in the Dvali-Gabadadze-Porrati (DGP) model. In the general case, for theories with μ(a, k), we obtain a perturbative expansion for β(μ) around the general relativity case μ = 1 which, for f(R) theories, reaches an accuracy below 1%. Finally, as an example we apply the obtained fitting functions in order to forecast the precision with which future galaxy surveys will be able to measure the μ parameter.