  We discuss the dynamics of the universe within the framework of Massive
Graviton Dark Matter scenario (MGCDM) in which gravitons are geometrically
treated as massive particles. In this modified gravity theory, the main effect
of the gravitons is to alter the density evolution of the cold dark matter
component in such a way that the Universe evolves to an accelerating expanding
regime, as presently observed. Tight constraints on the main cosmological
parameters of the MGCDM model are derived by performing a joint likelihood
analysis involving the recent supernovae type Ia data, the Cosmic Microwave
Background (CMB) shift parameter and the Baryonic Acoustic Oscillations (BAOs)
as traced by the Sloan Digital Sky Survey (SDSS) red luminous galaxies. The
linear evolution of small density fluctuations is also analysed in detail. It
is found that the growth factor of the MGCDM model is slightly different
($\sim1-4%$) from the one provided by the conventional flat $\Lambda$CDM
cosmology. The growth rate of clustering predicted by MGCDM and $\Lambda$CDM
models are confronted to the observations and the corresponding best fit values
of the growth index ($\gamma$) are also determined. By using the expectations
of realistic future X-ray and Sunyaev-Zeldovich cluster surveys we derive the
dark-matter halo mass function and the corresponding redshift distribution of
cluster-size halos for the MGCDM model. Finally, we also show that the Hubble
flow differences between the MGCDM and the $\Lambda$CDM models provide a halo
redshift distribution departing significantly from the ones predicted by other
DE models. These results suggest that the MGCDM model can observationally be
distinguished from $\Lambda$CDM and also from a large number of dark energy
models recently proposed in the literature.
