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For a class of viable cosmological models in $f(R)$ gravity which deviationfrom the Einstein gravity decreases as a inverse power law of the Ricci scalar$R$ for large $R$, an analytic solution for density perturbations in the mattercomponent during the matter dominated stage is obtained in terms ofhypergeometric functions. An analytical expression for the matter transferfunction at scales much less than the present Hubble scale is also obtained.

Analytic solution for matter density perturbations in a class of viable cosmological f(R) models