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dependence in future. 

## IV. CONCLUSION 

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In the present paper we have numerically calculated the evolution of both homogeneous background and density fluctuations in a viable f ( R ) model of accelerated expansion based on the specific functional form proposed in Ref. [5]. We have found that viable f ( R ) gravity models of accelerated expansion generically exhibit phantom behavior during the matter- dominated stage with crossing of the phantom boundary w$_{DE}$ = − 1 at redshifts z ≲ 1. The predicted time evolution of w$_{DE}$ has qualitatively the same behaviour as that was recently obtained from observational data in [2]. 

As for density fluctuations, we have numerically confirmed our previous analytic results on a shift in the power spectrum index for large wavenumbers which exceed the scalaron mass during the matter dominated epoch[6], while for smaller wavenumbers fluctuations have the same amplitude as in the ΛCDM model. 

We have also investigated the growth index γ ( k, z ) of density fluctuations and have given an explanation of its anomalous evolution in terms of time dependence of G$_{eff}$ . Since γ has characteristic time and wavenumber dependence, future detailed observations may yield useful information on the validity of f ( R ) gravity through this quantity, although current constraints have been obtained assuming that it is constant both in time and in wavenumber[3, 10]. 

