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Why are gravitationally bound systems unaffected by cosmological expansion?

Is it because on local scales gravity has overcome the effects of the expansion of space and thus enabled localised clustering of matter into star systems, galaxies, etc. that remain in a bound configuration, unaffected by the expansion of space due to the overwhelming force of gravity?

Or, is it simply that empirically it is observed that the expansion of space occurs on cosmological scales, and this is described well by an FRW universe. However, this assumes that homogeneity and isotropy hold, which is only true on the largest scales (I think $\sim$ 50 megaparsecs?!). Clearly more locally, such assumptions don't hold, and for example, in our own solar system the Schwarzchild solution (to Einstein's field equations) agrees well with observational data, and importantly, doesn't predict any expansion of space?!

Or, is there some other explanation that I'm missing?!

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  • $\begingroup$ I am no expert, but your first paragraph is correct, AFAIK, but stating Clearly more locally, such assumptions don't hold, and for example, in our own solar system the Schwarzchild solution (to Einstein's field equations) agrees well with observational data, and importantly, doesn't predict any expansion of space?! may not hold up, (and again this is outside my knowledge bubble), the Schwarzchild solution is an aid to understanding GR rather than anything physically real, as angular momentum is conserved, so black holes all spin. But there should be duplicates here already, lot of them. $\endgroup$
    – user140606
    Commented Jan 10, 2017 at 0:04
  • $\begingroup$ Gravitationally bound systems are not expanding today. But we know that they did expand at some point of time. Otherwise they should have been all at one point of space, individually as well as all of them together. This means they stopped expanding at some point/event, $\endgroup$
    – kpv
    Commented Jan 10, 2017 at 7:17
  • $\begingroup$ @kpv Is the reasoning that, in the early universe, there were regions of space with slightly denser concentrations of matter and over time more nearby matter was attracted to these regions due to gravity, and then at some point the gravity within this region was strong enough to overcome the initial expansion due to the Big Bang, thus halting any local expansion within these denser regions and allowing the formation of a hierarchical structure of star systems, galaxies and galaxy clusters?! $\endgroup$
    – user35305
    Commented Jan 10, 2017 at 9:11
  • $\begingroup$ @kpv .... Is the reason why galaxy clusters (or superclusters) are the largest gravitationally bound structures one observes because this is the largest scale at which gravity is able to overcome the "outward" expansion of space?! $\endgroup$
    – user35305
    Commented Jan 10, 2017 at 9:50
  • $\begingroup$ @user35305: No body knows. This is area of speculation. My speculation is that gravity must have gone missing for a very short moment. Otherwise Big Bang and expansion would not have happened. It must have returned immediately after and started to control things again. Due to this tiny moment of gravity self destructing itself, big bang/inflation/expansion would have been possible. Of which expansion is still surviving and fluctuating between accelerated and slowed down. Gravity is last force to disappear and first one to return. It never dies, it just blinks a big bang. $\endgroup$
    – kpv
    Commented Jan 10, 2017 at 21:25

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[Measured velocities vs distance up to 20 Mpc1

Your second paragraph is mostly right. But let's be a little more precise because it's easy to be misled. B

You are right that at about 50 to 100 megaparsecs (Mpc) you see pretty strongly the statistical homogeneity and isotropy, and can measure the expansion of the universe from the redshift due to the velocities of galaxies at those distances. In fact, you can do better, and even at a few Mpc and for sure 10 you can see the expansion, with more distant galaxies receding from us faster than those closer in. See for instance a graph of the Hubble velocity/distance graph for relatively close in galaxies, as shown above. But also notice the non statistical spread in the blue ellipsoidal area: those are different galaxies, 'HELD' together by their self gravity in the Virgo Cluster. Averaging those things out it gets more consistent at larger distances. That is from the wiki articles on the Hubble expansion at https://en.m.wikipedia.org/wiki/Hubble's_law#/media/File%3AHubble_constant.JPG

Hubble has to do it with much closer in data, un to 2 Mpc, that is what he could confidently measure in 1929. See his plot right below. The expansion was thus suspected and accepted to some extent, but not really fully unit more measurements were done. The coup de grace was the discovery of the CMB radiation indicating that there had been a Big Bang.

Hubble's expansion plot data

The local effects dominate because the gravitational fields from nearby galaxies are just much stronger than that from much further away, even if there's a lot of them. You see that in the data for the Virgo galaxies in the first figure above. As for the earth, the gravitational pull of the Sun is more than that from other stars in the Milky Way, or nearby galaxies like Andromeda. We do have some galactic neighbors, and are part of a galactic cluster. All of those have some influence and in fact our whole galactic cluster has a peculiar velocity with respect to the average cosmological expansion. We have to subtract the effect of the earth's peculiar velocity with respect to that average motion to make sure our CMB measurements are then in a coordinate frame that is comoving with the universe, and it is from which the universe looks isotropic and homogeneous, on the average. The CMB has been probably the best way to get to that peculiar velocity which then makes us, after subtracting it, see the CMB as homogeneous and isotropic as possible. That peculiar velocity is about 360 km/sec in the direction of the constellation Leo. See the parts that have to be added together to obtain out total local velocity with respect to the average motion of the universe's expansion at http://image.gsfc.nasa.gov/poetry/ask/a10552.html

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  • $\begingroup$ So what is the exact reasoning for why gravitationally bound systems such as star systems don't expand? Is it simply because gravity has long since overwhelmed the initial expansion due to the Big Bang in these denser regions, enabling structure to form. Does expansion only continue to occur on larger scales in regions of much lower (matter) density and in the voids between galaxy clusters?! Is the reason why galaxy clusters are the largest scale structures we observe because beyond this gravity cannot overcome the "outwards" expansion of space?! $\endgroup$
    – user35305
    Commented Jan 10, 2017 at 9:00
  • $\begingroup$ Gravity contributes at all scales. Expansion tends to pull them apart and more local gravity tends to pull it together. In the evolution of structure, you have to put in the local density excesses (where some matter already started pulling together, and it starts with quantum fluctuations), and evolve the equations to see what dominates, how long it takes, at each size. It forms first at scales like cluster and later smaller like stars. It is at all scales a trade off between expansion, density and size of density excesses. Random cosmological quantum fluctuations start the large scale $\endgroup$
    – Bob Bee
    Commented Jan 10, 2017 at 19:48
  • $\begingroup$ The quantum fluctuations were from the early Planck times and we see them in the CMB. Dark matter contributed to the matter density because it had gravity but no electromagnetism to disperse things. The equations are semi classical for the size of instabilities, called Jeans instability, and favors larger sizes. But the expansion did not allow, at each instant, the formation of structure at sizes comparable to the Hubble distance where expansion predominated. The whole topic of fallacy and cluster formation still has some unanswered questions and research. See the cosmology book by Dodelson $\endgroup$
    – Bob Bee
    Commented Jan 10, 2017 at 19:54
  • $\begingroup$ Thanks for the details. So, is it correct to say that as the density perturbations seeded in the early universe grew the local gravity began to dominate over the effects of cosmological expansion enabling localised structures to form. Such gravitationally bound systems are unaffected by cosmological expansion, since the gravity of such localised systems overwhelms the effects of this expansion?! $\endgroup$
    – user35305
    Commented Jan 10, 2017 at 20:34
  • $\begingroup$ ... Why is it that galaxy superclusters are the largest possible structures before cosmological expansion dominates? Is it simply because one considers the gravitational pull from the average centre of such superclusters is only just strong enough to keep such structures gravitationally bound and anything beyond this size gravity is too weak to prevent cosmological expansion from taking over?! $\endgroup$
    – user35305
    Commented Jan 10, 2017 at 20:39

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