Avoiding structure collapse due to dark energy?

I had a question about this paper (https://arxiv.org/abs/1401.3742)

There, the authors indicate that dark energy competes against gravity in oversdensities and can slow down or even prevent their collapse.

I have a simple question about this:

Galaxies will in principle evaporate their outer layers and their innermost ones will collapse under graviational forces and the relaxation of the orbits around the galactic nucleus through tidal forces and graviational waves emission. However, can there be galaxies (or other structrues) where the "fight" between gravity and dark energy can stabilize these structures indefinetely preventing their evaporation and gravitational collapse (assuming no external perturbations occur) despite the influence of tidal forces, gravitational waves emission...etc?

Intuitively I would say that the dark energy effect on the distance scale of a single galaxy is too small to prevent the processes you describe. (Note that putting a star on an escape trajectory due to interactions with other stars should be slightly easier in the presence of dark energy.) However, I have not done the math. I'll read the paper you reference when I get a chance to see if there are any relevant calculations in it.

PeterDonis said:

Intuitively I would say that the dark energy effect on the distance scale of a single galaxy is too small to prevent the processes you describe. (Note that putting a star on an escape trajectory due to interactions with other stars should be slightly easier in the presence of dark energy.) However, I have not done the math. I'll read the paper you reference when I get a chance to see if there are any relevant calculations in it.

Thank you. Perhaps this would be more suitable for bigger structures like clusters?

Suekdccia said:

Perhaps this would be more suitable for bigger structures like clusters?

Possibly. However, what I said about putting an object on an escape trajectory would be even more true for a bigger structure. So I don't think dark energy can suppress "evaporation"; instead it should enhance it.

As for gravitational collapse, a bigger structure isn't going to collapse all at once, its collapse will be galaxy by galaxy. So you would have to look at the effects of dark energy on a much smaller scale with regard to collapse. On that scale, it might slow down the collapse by a small amount, but it won't prevent it.

Of course, it's possible that a dark energy equation of state with a ##w## much less than ##-1## might change things; the paper is basically trying to constrain the possible values of ##w## by looking at structure formation and stability. But given that ##w## is within the range they find to be compatible with the structures we see today, I don't think dark energy can significantly change the longer term processes you describe; those processes (at least if we want them to go to completion, i.e., structures like the ones we see today are entirely either evaporated or collapsed) happen on a time scale that we haven't probed yet (the universe isn't old enough), so we can't rule them out just because dark energy is within the range that is consistent with the structures we see today.