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Does dark energy expand galaxies slightly over time? I would think this could be verified easily (observe if galaxies far away / further in the past smaller and denser), and might make a good research topic!

I am specifically asking at the galaxy level here. It is pretty clear dark energy acts at levels beyond a galaxy.

Edit: There have been similar questions pointed out, but I have not seen any asking specifically at the level of a galaxy.

Note: It would seem that if the galaxies used to be smaller, that might explain the increased star formation explained here: https://webbtelescope.org/webb-science/galaxies-over-time "About 10 billion years ago, galaxies were more chaotic, with more supernovae, 10 times more star formation"

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    $\begingroup$ Answered here physics.stackexchange.com/questions/2110/… $\endgroup$ Commented Dec 11, 2021 at 13:46
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    $\begingroup$ Does this answer your question? Does the gravity oppose to the Universe expansion? $\endgroup$
    – PM 2Ring
    Commented Dec 11, 2021 at 20:28
  • $\begingroup$ Sort of, but it seems the answer here and in the prior comment's answers contradict. It seems it could be figured out by seeing if galaxies were tighter together in distant history (e.g. examine the Hubble Deep Field imagery). It seems like it could be an answer to why Quasars used to be a thing, but not anymore, if the stars have been moved further from the super massive galactic center black holes. $\endgroup$
    – Jonathan
    Commented Dec 12, 2021 at 2:31
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    $\begingroup$ Expansion is really weak, so you need a lot of distance to get significant expansion. Inside a galaxy, gravity prevents expansion. As Pela said, "on scales as small as galaxies, and even galaxy groups, space doesn't expand at all. Gravity prevents galaxies from expanding, and keeps galaxies near each other from receding". $\endgroup$
    – PM 2Ring
    Commented Dec 12, 2021 at 3:20

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TLDR: Dark energy drives the accelerated expansion of empty space between galaxy clusters. Other effects dominate the dynamics within a given cluster.

If I can get philosophical for a moment, we must remember that every equation we write down is an approximate description of nature built from simplifying assumptions and with a well defined domain of validity. So what is the domain of validity for dark energy?

cosmology as dust in the wind

When we derive the Friedmann equations from the FLRW metric, we assume that the contents of the universe have uniform density. The matter of the universe is modeled as a uniform, non-interacting dust. In this case the dust grains are galaxy clusters. By "non-interacting" we mean the galaxy clusters just sit in place unless they are carried around by the cosmological dynamics. Just dust in the wind, man.

Dark energy fits into the Einstein field equations as a cosmological constant. It has a constant energy density.

In the past the dust grains were closer together, and the universe was matter dominated. The cosmological dynamics were driven primarily by the matter in the universe. As the universe expanded, there became more empty space between the dust grains. The matter density of the universe decreased. Eventually the matter density got down to a similar scale as the dark energy density. At this point dark energy, starts to noticeably affect the cosmological dynamics. As the universe expands more, the matter density continues to decrease, but the dark energy density stays the same, leading to the dark energy dominated cosmology we see today.

The Friedmann equations describe the dynamics of galaxy clusters. That is their domain of validity.

inside a grain of dust

If we zoom in on a single grain of dust and look inside, we'll find many galaxies. The key thing to understand is that at the scale of a single galaxy cluster, the spacetime isn't dark energy dominated. The average density of matter in a cluster is way bigger than the average density of the universe. There's just way more empty space between clusters than between galaxies within a cluster.

If we apply the same cosmological assumptions at this scale the dynamics would be different than for galaxy clusters. The increased matter density means the expansion won't happen at the same rate. The rate of expansion between clusters is larger than the rate of expansion between neighbor galaxies which is larger than the rate of expansion between stars within a galaxy.

The non-interacting assumption certainly doesn't hold within a cluster. The galaxies are not just floating on the wind of cosmology, they are interacting gravitationally and affecting each other. In this case we might have to worry about solving the gravitational $N$-body problem with a non-zero cosmological constant.

The Friedmann equations which describe cosmology are not a useful approximation of the dynamics inside a galaxy. The cosmological constant (dark energy) modifies the gravitational dynamics, but it does not drive accelerated expansion in the same way it does for the empty space between galaxy clusters.

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    $\begingroup$ Totally agree that dark energy is not dominant, but that isn't really aaswering the question; it is arguing that the scale factor of a galaxy doesn't increase as fast as the scale factor in the Friedmann equations. $\endgroup$
    – ProfRob
    Commented Dec 14, 2021 at 15:59
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    $\begingroup$ As a GR noob, the discussion in proximity to "The rate of expansion between clusters is larger than the rate of expansion between neighbor galaxies which is larger than the rate of expansion between stars within a galaxy..." better answers my questions in Physics SE than the current answers! Would order 1AU metric expansion of space begin if the solar system were not inside a galaxy? and Is the metric expansion of space relatively uniform on different length scales? No balloons/raisin bread! $\endgroup$
    – uhoh
    Commented Dec 14, 2021 at 20:39
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    $\begingroup$ @uhoh Thanks for the share! The answer of the first question seems to confirm (with expanded orbit radius) that the solar system would expand over time, slightly. It would seem to me that the same reasoning would make the galaxy larger over time (increased orbit radius of stars around the galaxy). Anyone care to elaborate? $\endgroup$
    – Jonathan
    Commented Dec 17, 2021 at 3:22
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When you write down the Friedmann equations for the FLRW metric, you'll see that dark energy was not dominant in the past.

The energy densities evolve like this;

$$\Omega_{r} = \Omega_{r,0}(1+z)^4,~\Omega_{m}=\Omega_{m,0}(1+z)^3,~\Omega_{\Lambda} = \Omega_{\Lambda,0}~~$$

This shows us that, as you go past in time ($z \rightarrow \infty$), first matter and then radiation dominate the dynamics of the universe. The dark energy only recently started to show its effects. You can even calculate that time by just equating $\Omega_m = Omega_{\Lambda}$.

$$\Omega_{m,0}(1+z)^3 = \Omega_{\Lambda,0}$$ for $\Omega_{m,0}=0.3$, $ \Omega_{\Lambda,0} = 0.7$, we obtain $z=0.326$.

So for $z \gg 0.326$, the universe was matter-dominated, and as you go in the past, the effect of the dark energy becomes less and less.

Another problem with your argument is the 'expansion of the universe.' You can think of galaxies as points carried by the expansion of space and not expanding with the space itself. Think about galaxies as points embedded on the surface of the balloon. As you inflate the balloon, the distance between the points increases, but nothing happens to those points. This is an excellent analogy to understand how the universe's expansion works.

So to sum it all up;

  1. The dark energy was not effective until recently, so it cannot affect the dynamics of the early universe.
  2. The galaxies do not get affected by the expansion of the universe.
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  • $\begingroup$ Are we sure galaxies are not affected? If space is stretched 2x in the universe, it would seem that galaxies would be stretched 2x as well. While galaxies are small in comparison to the universe, they aren't exactly points either - they are quite large - hundreds of thousands of light years across. While dark energy wasn't dominant in early history, it was still there. $\endgroup$
    – Jonathan
    Commented Dec 12, 2021 at 12:55
  • $\begingroup$ @Jonathan. Well, yes, we are. Yes, the dark energy was still there, but it was not effective. The galaxies are drifting while the universe expands. It does not affect them. It requires a significant amount of energy to separate gravitationally bounded systems. Let's say you take a balloon and put an ant on it. Once the balloon is twice its size, the ant will not be twice its size. You can think of the expansion of space as such. What happens is the ant drifts along with the balloon. $\endgroup$
    – seVenVo1d
    Commented Dec 14, 2021 at 9:08
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    $\begingroup$ I agree with #1 but #2 (which is what the question is asking) is just an assertion. Galaxies are not point-like. $\endgroup$
    – ProfRob
    Commented Dec 14, 2021 at 15:57
  • $\begingroup$ @ProfRob In certain scales/approximations, can't we treat them as point particles.Cause I have seen such approximations. $\endgroup$
    – seVenVo1d
    Commented Dec 17, 2021 at 12:52
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One way to think about this is that dark energy begins to have an impact when its energy density becomes comparable to the energy density of matter (or radiation). The energy density of dark energy is about $7 \times 10^{-30} g/cm^3$, which is much smaller than the density of interstellar space (~one hydrogen atom per cubic centimeter). So galaxies don't expand.

The dark energy energy density is larger than the density of intergalactic space (which is about $1 \times 10^{-30} g/cm^3$), and hence this is where the expansion happens.

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  • $\begingroup$ Agree with this, but it isn't answering whether galaxies expand "slightly over time". $\endgroup$
    – ProfRob
    Commented Dec 14, 2021 at 16:01

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