An analytic calculation of the growth index for $f(R)$ dark energy model

Abstract

We derive the analytic formula of the growth index for $f(R)$ dark energy model where the effect on the growth of matter density perturbation ${\delta }_m$ from modified gravity (MG) is encoded in the effective Newton coupling constant $G_{\mathrm{eff}}$ in MG (or equivalently $g\equiv G_{\mathrm{eff}}/G$). Based on the analytic formula, we propose that the parameter $g$ can be directly figured out by comparing the observed growth rate $f_g\equiv d\ln {\delta }_m/d\ln a$ to the prediction of $f_g$ in general relativity.

5 pages, 1 figure; refs added; minor revised, version accepted by EPJC

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Cited by in corpus (4)

• Linearized physics and gravitational-waves polarizations in the Palatini formalism of GBD theory
• Linearized modified gravity theories and gravitational waves physics in the GBD theory
• Configurational Entropy in Chaplygin Gas Models
• Scalar perturbation and density contrast evolution in $f(Q,C)$ gravity