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.

I wasn't talking about using the FRW model to model something like the solar system. I was talking about using the Schwarzschild-de Sitter model, which is different: it is basically a model of an isolated gravitationally bound system in the presence of a cosmological constant, which, with a suitably chosen (very small) value of the cosmological constant, is a reasonable approximation to a model of a bound system like the solar system in our universe.

Whereby regarding the cosmological constant there seems to be a bridge to the FRW model in this approximation.

I understand that one can't model a bound system using the FRW model. Would you say that any considerations by interpreting the Friedmann equations locally like I attempted in #41 don't make any sense? Strictly these equations are based on the assumption of ideal homogeneity. I'm interested if they nevertheless provide conclusions regarding local inhomogeneities such, as regions with "overdensity" don't participate in the accelerated expansion or as super voids would expand faster than the universe in average.

You would want to use the value for the cosmological constant that corresponds to our best current FRW-based model, yes.

You can interpret the Friedmann equations locally, but you have to meet the conditions, one of which is that the density is the same everywhere. If that condition is not met, the equations aren't valid. But if, for example, you have a spherically symmetric (another condition for the FRW model to be valid) "bubble" of uniform density inside a spherically symmetric universe of some other density, you can apply the Friedmann equations inside the "bubble" just fine. The problem with applying the Friedmann equations locally in our actual universe is that the density is very, very far from being uniform on local scales.

There is ongoing work to develop more sophisticated models, not using the precise FRW metric (but the models could be, I think, described as FRW plus perturbations), that allow for variations in density. But AFAIK nobody has tried to apply them on scales as small as a single galaxy; we are still talking scales of tens to hundreds of millions of light years.

Simply a measure of rate of change or duration. It isn't some mythical substance but another property. Even under spacetime as per GR this definition does not change.

You're the one that made statements about what it is. I just asked you to make up your mind which of the two inconsistent things you said you want to pick.

As far as GR is concerned, time is just like length, except it's measured along timelike curves instead of spacelike curves.