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Resumen:
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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) = ?^(?)_(m)(a) with ? ? 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 ?(a, k) = G_(eff)/G and show that f(a) = ?(a) ?^(?)_(m)(a) provides fits to the numerical solutions with similar accuracy to that of ACDM. In the time-independent case with ? ¼ ?ðkÞ, simple analytic expressions for ?ð?Þ and ?ð?Þ are presented. In the time-dependent (but scaleindependent) case ? = ?(a), we show that ?(a) has the same time dependence as ?(a). As an example, explicit formulas are provided in the Dvali-Gabadadze-Porrati (DGP) model. In the general case, for theories with ?(a, k), we obtain a perturbative expansion for ?(?) around the general relativity case ? = 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 ? parameter.
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