%0 Journal Article
%A Aparicio Resco, Miguel
%A López Maroto, Antonio
%T Parametrizing growth in dark energy and modified gravity models
%D 2018
%@ 2470-0010
%U https://hdl.handle.net/20.500.14352/12038
%X 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.
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