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Concerning cosmological structures (like galaxies, clusters of galaxies, gas bodies, superclusters...etc) if the elements that make them are close enough they will be attracted towards each other by gravity. Contrarily, if they are sufficiently far apart they will get further away following the expansion of the universe.

However, sometimes, even if objects follow the expansion of the universe, under some conditions, they can "de-attach" from it and start being attracted to each other by gravity.

Is it possible that these cosmological structures may follow a cycle between expansion and contraction? I mean, is it possible that a structure expands with the Hubble flow, then it stops and starts shrinking, and then, somehow, after collapsing, starts following the Hubble flow repeating this cycle indefinitely? Has this been ever observed?

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    $\begingroup$ Has this been ever observed? This (if it happened) would happen on an enormous timescale so I don't know what you'd consider an observation in that case. $\endgroup$ Commented Jan 14, 2023 at 2:26

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This seems rare in the standard cosmological model. The reason is that to get a detachment from the Hubble flow masses need to move near each other so their mutual attraction overwhelms the Hubble flow - but now they are gravitationally bound.

However, n-body dynamics still applies: a galaxy cluster that is bound can still eject parts. So we can imagine a galaxy flowing away, getting close enough to other galaxies to form a cluster, and then be ejected and rejoining the Hubble flow.

I think this will already be a rare occurrence: it is not that common for galaxies and other objects to have aligned velocities so they can bind, and most stuff in a cluster tends to move inward (it is the light objects that tend to be ejected).

But more importantly, accelerating expansion means that velocities in the co-moving frame will seem to diminish exponentially: there are going to be less other things to bind to that can be reached. The amount of stuff you can interact with over the future decreases as the event horizon moves closer. So repeating this sequence of capture/n-body encounter/ejection many times will be very rare.

This is also individual objects rather than entire structures. A cluster coalescing by infalling galaxies will potentially pulsate as they pass through each other, slow down, and fall back in. But that is still a bound process. Some outlying objects are likely to escape, but the distances to other stuff to bind to are increasing exponentially with time so it is unlikely they will ever catch up.

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