Newtonian Analog to Expanding Universe

Simple sphere containing rocks moving outwards with a Hubble flow pattern. The dynamics of the expansion is equivalent to the expanding Universe.

 

Birkhoff's theorem says that within an isotropic universe, in GR you can carve out a sphere and the dynamics of events occurring within this sphere are independent of the matter outside the sphere. Hence, one can follow an expanding small sphere with Newtonian physics and this will replicate the expansion of the entire universe.