I The Evolution of Galactic Scale Cosmic Voids

Suekdccia
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Collapse and expansion of Galactic Scale Cosmic Voids
According to some papers I've found [1], [2] expanding voids can be found inside clouds of denser materials that can cause them to eventually collapse. I have a question about this:

Overdensities generally expand up to a given turnaround radius and then collapse. However, as the elements in the overdensity would have been gravitationally bound since the beginning, the expansion would not actually be driven by dark energy. The void however, would expand faster than the overdensity as the interior would have a very low density, and theoretically would not be gravitationally bound, so the expansion of the void would be driven by dark energy. If this is correct, when the void would collapse because of the surrounding overdensity, would the matter be "pushed" to collapse from a greater distance (as it would have been "moved" by dark energy), therefore gaining more kinetic energy than in the rest of the overdensity?

So, if the fate of a void inside an overdensity is ultimately collapse, as they expand more than the overdensity the radius of the void will grow more quickly. So, when it collapses, and the matter from the outskirts of the void smashes and collapses, shouldn't that region be hotter than the rest of the overdensity, as it run more distance until collapsing (therefore gaining more kinetic energy from potential energy)?


[1]: https://academic.oup.com/mnras/article/350/2/517/1115675

[2]: https://arxiv.org/abs/1501.02120
 
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