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 $\Lambda$CDM cosmology, with errors below $0.25\%$, is given by $f(a)={\Omega }_m^{\gamma }(a)$ with $\gamma \simeq 0.55$. 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 $\mu (a,k)=G_{eff}/G$ and show that $f(a)=\beta (a){\Omega }_m^{\gamma }(a)$ provides fits to the numerical solutions with similar accuracy to that of $\Lambda$CDM. In the time-independent case with $\mu =\mu (k)$, simple analytic expressions for $\beta (\mu )$ and $\gamma (\mu )$ are presented. In the time-dependent (but scale-independent) case $\mu =\mu (a)$, we show that $\beta (a)$ has the same time dependence as $\mu (a)$. As an example, explicit formalae are provided in the DGP model. In the general case, for theories with $\mu (a,k)$, we obtain a perturbative expansion for $\beta (\mu )$ around the General Relativity case $\mu =1$ 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 $\mu$ parameter.

12 pages, 12 figures. New section on applications to forecasts for galaxy surveys and new references included. Matches version published in PRD

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Cited by in corpus (8)

• J-PAS: forecasts on dark energy and modified gravity theories
• An Accurate Fitting Function For Scale-dependent Growth Rate in Hu-Sawicki $f(R)$ Gravity
• Subpercent Accurate Fitting of Modified Gravity Growth
• Versatile parametrization of the perturbation growth rate on the phantom brane
• Modified gravity versus shear viscosity: imprints on the scalar matter perturbations
• Constraining Scale Dependent Growth with Redshift Surveys
• Testing for gravitational preferred directions with galaxy and lensing surveys
• J-PAS: forecast on the primordial power spectrum reconstruction