As I understand it the FRW model predicts the dynamical evolution of the universe globally thereby assuming an average matter density. In our universe the data are consistent with the assumption of a small cosmological constant. In the milky way however the matter density is higher than the critical density. I'm not sure if the Friedmann equations can be applied locally. If yes then it seems that from this point of view the milky doesn't participate in the global expansion. Hm, perhaps overdensity and gravitationally bound means the same.