Expanding/non-expanding space

Question

Due to inflationary cosmology space on a large distances expands. However on small distances (locally) we do not record any expansion. Thus there must be a region, domain or a "border line" which separates expanding and non-expanding space. How do we detect or calculate the border between expanding and not expanding space? and what is the physics in that region of transient from non expanding to expanding space?

Answer 1

The current rate of expansion according to our most accepted model is around $68\ \mathrm{(km/s)/Mpc}$. That is, every second, a distance of 1 megaparsec will gain about 68 kilometers. 1 megaparsec is around $30.86$ quintillion kilometers. On distance scales relevant to humans, let's say around $30\ \mathrm{AU}=4500000000\ \mathrm{km}$, you'd expect that you'd gain about $0.313\ \mathrm{km}$ per year. That's less than our current measurement uncertainty, but you'd think that we'd notice it after a few decades, right? Problem is that our little corner of space is gravitationally bound. The density of matter around us is sufficiently high to keep the expansion of space to a minimum. It's not really necessary for there to be a point where expansion stops entirely; it's effects on small scales are so weak that the smallest force is enough to overcome it.

So is there a border line? Perhaps. Some cosmologists will tell you that near us the density of energy is greater than the critical density, which means space will eventually stop expanding and start contracting (technically only true if that space not only has closed curvature, but also only if that curvature is large enough to induce contraction, which isn't a guarantee (pay no attention to the technical bits in the asides)). Other cosmologists will tell you that there aren't any regions (within reason) that we can identify as non-expanding space. Assuming a flat spacetime, an over-density of matter slows expansion more, but never completely stops it.

Really, it's not something we could even measure. Our instruments are not sensitive enough to measure the rate of expansion across distances the size of the Solar system or smaller even assuming the full blown value of expansion ($68\ \mathrm{(km/s)/Mpc}$).

That should answer the question of the difference in physics. There isn't any measurable difference. If the effects of full bore expansion are too minimal to notice on human scales, then we shouldn't expect any difference in the physics on those scales for regions that hypothetically experience no expansion. And if there are no such regions, then this all becomes an exercise in imagination, but fun nonetheless.