> How do we know that galaxies are accelerating away from us and not moving at constant speed?
More precisely, we see that galaxies started accelerating away from us a few billion years ago; before that they were decelerating (moving away from us but with the "speed" decreasing instead of increasing).
> People often point to the observation that the further away a galaxy is, the faster it appears to be moving away from us, implying acceleration.
That observation tells us that the universe is expanding, but by itself it does not tell us whether the expansion is accelerating or decelerating or neither. So you are correct that that observation alone is not sufficient to show that the expansion is accelerating.
What we look at to see how the expansion rate changes with time is a comparison of three pieces of observed data, galaxy by galaxy: redshift, brightness, and angular size. The relationship between these three quantities is what cosmologists use to construct a model of the expansion history of the universe, which in turn tells us things like what I said above, that the expansion has been accelerating for the last few billion years but before that it was decelerating.
Meaning, why did the expansion change from decelerating to accelerating a few billion years ago? Because that was when the density of matter, which had dominated the dynamics until then, became smaller than the density of dark energy, which has dominated the dynamics since then. The dark energy density doe not change with time, but the density of matter decreases as the universe expands.
How is is that dark energy density does not change with time? Surely the total amount of dark energy has to be constant (energy can't be created or destroyed, and all that), and then as the universe expands, that's then the same amount of energy over a larger volume, right?
Dark energy may be the energy of vacuum itself, that's why it's constant. And no, energy conservation does not apply in this case. There is a good blog article on precisely this question by Sean Carroll: https://www.preposterousuniverse.com/blog/2010/02/22/energy-...
> How is is that dark energy density does not change with time?
Because that's how a cosmological constant works.
There are alternate models where there is "dark energy" (as in, stress-energy that causes accelerated expansion) whose density does change with time (for example, a "Big Rip" model in which the dark energy density increases with time), but such models do not match our best current data.
I think the story is that dark energy is indeed created, in the new emptiness resulting from the expansion of space.
<mumble> I believe it's supposed to be spacetime that expands, not 'space'. But it's beyond me to explain what that even means; as I understand it, spacetime refers to the whole Universe, across all of time. To 'expand' means 'to become larger over time'. But if the thing that's expanding includes time itself, then I'm bewildered.
It is in fact the metric expansion of space. The spatial part of the Robertson-Walker spacetime metric expands equally along the time axes of a family of freely-falling future-directed worldlines (we can call them "Eulerian observers", and individual clusters of galaxies are good approximations).
That is, in the past, galaxy clusters are relatively close together, and in the future they are relatively very far apart.
If you need an image, think of a vase of cut flowers, with the stems tightly bound together at the bottom of the vase, and the flowers loosely separated at the top. Time is in the direction away from the vase's bottom. A super thin slice through a stem represents a snapshot of a galaxy cluster at a particular time in its existence.
More precisely, we see that galaxies started accelerating away from us a few billion years ago; before that they were decelerating (moving away from us but with the "speed" decreasing instead of increasing).
> People often point to the observation that the further away a galaxy is, the faster it appears to be moving away from us, implying acceleration.
That observation tells us that the universe is expanding, but by itself it does not tell us whether the expansion is accelerating or decelerating or neither. So you are correct that that observation alone is not sufficient to show that the expansion is accelerating.
What we look at to see how the expansion rate changes with time is a comparison of three pieces of observed data, galaxy by galaxy: redshift, brightness, and angular size. The relationship between these three quantities is what cosmologists use to construct a model of the expansion history of the universe, which in turn tells us things like what I said above, that the expansion has been accelerating for the last few billion years but before that it was decelerating.