A viable f(R) gravity model without oscillations in the effective dark energy

In this study, we propose a reparametrization of a specific viable [Formula: see text] gravity model to represent it as a perturbation of the [Formula: see text]CDM model. The [Formula: see text] gravity model under consideration includes two parameters, [Formula: see text] and [Formula: see text], which control how close the proposed model can be to [Formula: see text]CDM, allowing for arbitrary proximity. Furthermore, it is shown that the Hu–Sawicki (HS) model is a limiting case of this reparametrized model. Following the existing literature, we also derive an analytical approximation for the expansion rate [Formula: see text], which shows an excellent agreement between this analytical approximation and the numerical solution over a wide range of redshifts for realistic values of the deviation parameter [Formula: see text]. By appropriately selecting values for the model parameters, we plot the cosmological parameters [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], as well as the statefinder quantities [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]. We find that their present values (at [Formula: see text]) are consistent with the observations from Planck 2018 and the values predicted by the [Formula: see text]CDM model. It is important to note that the examined cosmological and statefinder parameters do not exhibit significant oscillations of effective dark energy, which could lead to singular and unphysical solutions at high redshifts. This anomalous behavior has been avoided here by utilizing the approximate analytical solution for [Formula: see text]. Additionally, we conduct a detailed analysis of the evolution of matter density perturbations within the introduced [Formula: see text] gravity model. The results demonstrate that this viable [Formula: see text] gravity model is practically indistinguishable from the [Formula: see text]CDM model at the background level.