# Expanding/non-expanding space

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?

## 1 Answer

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.

• That is what is written in all textbooks on the subject. The illusion of so called space expansion started from mistake of Edwin Hubble when he interpreted his data via Doppler in order "to fit" Friedman solution. Geometry of space is Lobachevskian and locally can be approximated by Euclidean geometry. In Euclidean geometry parallel geodesics ( light rays) stay at fixed distance . In Lobachevskian geometry parallel geodesics spread apart at exponencial rate. That is why on local scales you do not see "space expansion" and large enough distances are needed to see geometric red shift. – Georg von Brzeski Apr 25 '17 at 15:37
• @GeorgvonBrzeski Yes, well I'm going to stick with only including what most textbooks say because this site prioritizes mainstream accepted theories, regardless the validity – Jim Apr 25 '17 at 17:46
• Jim , textbooks are written by people and people make crucial mistakes. Two Nobel prize laureates rejected principles NMR imaging because textbooks on optics say that having a wavelength L you can resolve the most L/2. That is correct in all optical conventional business. NMR uses L= about 300m so when inventors claimed to resolve centimeter details that sound they never red textbook. Problem is that L=300m but imaging is done via the Radon transform. So inventors went to investors and built the machine known today as Computed Tomography Scanner. – Georg von Brzeski Apr 28 '17 at 21:32
• @GeorgvonBrzeski I'm not sure what point you're trying to make. As I said, this site prioritizes mainstream accepted physics. It doesn't matter if that physics is right or wrong. The site merely presents what the current trends of physics follow, it doesn't judge the validity or come up with new physics. That said, as a cosmologist, I'm going with what I know from texts and my own personal experience with the mathematics because that is currently the most accepted physics. If you want to change that, write a paper and get most cosmologists to follow it. – Jim May 1 '17 at 12:19