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Examining the metric tensor used to explain expansion, I see no reason why the expansion should not occur everywhere, i.e. between molecules, between the planets, between the stars in a galaxy, etc. Yet apparently, only the galaxies are "locked into" the space portion of space-time, and only the proper distance between the galaxies is subject to red-shift analysis.

I have often thought that maybe the black hole seemingly at the center of each galaxy somehow locks a galaxy into the space portion of space-time and the use of the idea of "expanding space" doesn't apply to the space portion of space-time uniformly.

I apologize for any misuse of words here, e.g., "proper distance."

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marked as duplicate by John Rennie, user36790, CuriousOne, Cosmas Zachos, Diracology Jul 8 '16 at 23:12

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There are four forces that describe matter and energy in the universe. These forces are much stronger than the expansion of space. The raisin bread analogue is also good to understand this:

raisin bread

The raisins do not puff up as the bread does, because the electromagnetic cohesive forces of the raisin body maintain its volume since no yeast is working within the raisin. Analogously the galaxies are bound by gravitational forces and retain their identity. More so atoms and molecules which are bound by forces much stronger than just gravitational.

The expansion of space is sometimes described as a force which acts to push objects apart. Though this is an accurate description of the effect of the cosmological constant, it is not an accurate picture of the phenomenon of expansion in general. For much of the universe's history the expansion has been due mainly to inertia.

So it is a rough analogue but it gives a feeling.

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The gravity of the galaxy$^1$ holds it together; that is what keeps the distance between stars in a galaxy expanding. In other words, the gravitational pull of the galaxy overcomes the antigravity "pull" of the cosmological constant.

A good image is that of a couple groups of, say, five people. Each individual group has everyone standing in a circle and holding hands, but there is no connection between a group and the others. Now, have everyone move apart from everyone without letting go of the hands they are holding on to. The groups will move apart from each other, but within the groups, they won't get very far apart because they are holding hands. The groups are the galaxies, the air is space, and the people are stars/objects in the galaxy.

There are a few differences between the example above and real life, obviously. Stars are not holding hands; rather, gravity is a feature of spacetime. The Milky Way and the Andromeda Galaxy are actually coming closer to each other because of a strong gravitational pull between the two galaxies.

The galaxies are not "locked into" a portion of spacetime; forces overcome other forces. The stars of the Milky Way aren't glued to the fabric of spacetime. Rather, gravity controls their movements (and overcomes the expansion of the universe in the process).

Hope this helps!

$^1$It should also be noted that on an atomic scale, the nuclear forces prevent expansion. On the planetary level, it is still gravity holding things together.

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Your intuition is correct. There is no particular reason to assume any given region of space is not expanding, based on present data. However, measuring this on small scales is difficult. If we assume a very simplified version of expansion, we can get a numeric value for the expansion rate: $74.2 \frac{km/s}{MPc}$. Thus, a galaxy 10Mpc away from us would be moving away from us at 742km/s due to the expansion of space.

Andromeda is 0.66Mpc away from Earth. This means we might expect to see a mere 49km/s of movement due to the expansion of space. Given its apparent velocity away from us at 301km/s, this is measurable.

The nearest star, Alpha Centauri A is 0.000001339Mpc away from Earth. This means we might expect to see a 0.000099km/s (009.9cm/s) movement due to the expansion of the universe. Alpha Centauri is heading away from us at 18.6km/s (or 1860000cm/s). That's quite a brutal measurement to have to take!

The distance between us and the sun is 150 million kilometers, which is roughly 0.000000000004848 Mpc. Thus expansion of space between us and the sun could be expected to account for 0.0000000003597216km/s (359nm/s). For all intents and purposes, that velocity can be ignored in any meaningful calculation.

Now all of these assumed a very simple linear model for the expansion of space, but its sufficient to show just how insignificant the effects are no small scales. It's not that space isn't expanding everywhere, its that the effect is substantially overwhelmed by every other force out there, so we get away with not paying attention to it when making predictions.

Heck, for all we know, the expansion terms might even change as things get small. Its entirely possible that this simplified first order model isn't even a good model on the small scale. However, it shows just how substantial the higher order terms would have to be before we detected any effect at all from them.

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