Growth Index in the $γδ$CDM model

To better distinguish the nature of $H_0$ and $S_8$ tensions, it is necessary to separate the effects of expansion and the growth of structure. The growth index $γ$ was identified as the most important parameter that characterizes the growth of density fluctuations independently of the effects of cosmic expansion. In the $Λ$CDM model, analyses performed with various cosmological datasets indicate that the growth index has to be larger than its theoretically predicted value. Cosmological models based on $f(R)$ gravity theories have scale-dependent growth indices, whose values are even more at odds with the growth rate data. In this work, we evaluate the growth index in the $γδ$CDM model both theoretically and numerically. Although based on $f(R)$ gravity theory, we show through several analyses with different combinations of datasets that the growth index in the $γδ$CDM model is very close in value to the $Λ$CDM and the $ω$CDM models. The growth of structure is suppressed in the $γδ$CDM model, which is formulated with the extended gravitational growth framework. Upon analyzing cosmological data, we ascertain that the $γδ$CDM model is equally competitive as the $Λ$CDM and the $ω$CDM models.

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