Does dark energy make galaxies expand over long periods of time?

Question

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"

Answer 1

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.

Answer 2

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.

Answer 3

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.