First, let me emphasize that expanding space is not a physical phenomenon. It's a common misconception that there is something like the fabric of space, which expands over time, stretching out systems and carrying objects with it. Expanding space is just a convention that simplifies some of the mathematics in cosmological contexts. It represents a choice of coordinates on spacetime. It is not a physical process.

Since the idea of expanding space is a tenacious misconception, I've put a great deal of further reading at the bottom of this post.

That being said, the universe is expanding, and that means that objects are moving apart in a fairly uniform way, on average. At the largest scales, this expansion seems to be about the same everywhere (homogeneous) and the same in every direction (isotropic), but this is certainly not true at smaller scales. For cosmic voids -- regions less dense than the cosmological average -- their expansion has been slowed less by gravity than the universe at large, so they are expanding faster than average. Conversely, regions that are denser than average expand more slowly, due to their higher self-gravity, and they can even stop expanding and collapse. This collapse process is how galaxies are formed. Galaxies themselves consist of stably orbiting material and hence are not expanding or contracting (except to the extent that they are disturbed by newly accreted material).

Asymmetry in a system and its environment can also exert a tidal influence, which basically means that gravitational forces are different in different directions. This can cause the system to expand at a different rate in different directions, resulting in structures like filaments and sheets in the large-scale structure of the universe.

Regarding expanding space not being a physical influence, see for example this entry in the AskScience FAQ. If you prefer to hear it from eminent cosmologists, here is an excerpt from a 1993 interview with Steven Weinberg and Martin Rees:

> Popular accounts, and even astronomers, talk about expanding space. But how is it possible for space, which is utterly empty, to expand? How can ‘nothing’ expand?

> ‘Good question,’ says Weinberg. ‘The answer is: space does not expand. Cosmologists sometimes talk about expanding space – but they should know better.’

> Rees agrees wholeheartedly. ‘Expanding space is a very unhelpful concept,’ he says. ‘Think of the Universe in a Newtonian way – that is simply, in terms of galaxies exploding away from each other.’

> Narlikar puts it differently. ‘Space is not utterly empty: it has visible matter in the form of galaxies and also a lot of dark matter.’ Weinberg elaborates further. ‘If you sit on a galaxy and wait for your ruler to expand,’ he says, ‘you’ll have a long wait – it’s not going to happen. Even our Galaxy doesn’t expand. You shouldn’t think of galaxies as being pulled apart by some kind of expanding space. Rather, the galaxies are simply rushing apart in the way that any cloud of particles will rush apart if they are set in motion away from each other.’ The matter inside individual galaxies does not take part in the general expansion because it is held together by gravity.

Beyond these, here are articles discussing the point further:

(1) A diatribe on expanding space. This is pretty technical, but it's the most direct attack on the idea of expanding space. One key quote is that

> there is no local effect on particle dynamics from the global expansion of the universe: the tendency to separate is a kinematic initial condition, and once this is removed, all memory of the expansion is lost.

If a system is not expanding, then cosmic expansion is simply not relevant to it.

(2) The kinematic origin of the cosmological redshift. Very well written and less technical, although there are mathematical arguments. The main point of this article is that the cosmological redshift -- often framed as a consequence of space expanding -- is more directly just a Doppler shift. One of the introductory paragraphs reads:

> A student presented with the stretching-of-space description of the redshift cannot be faulted for concluding, incorrectly, that hydrogen atoms, the Solar System, and the Milky Way Galaxy must all constantly “resist the temptation” to expand along with the universe. One way to see that this belief is in error is to consider the problem sometimes known as the “tethered galaxy problem,” in which a galaxy is tethered to the Milky Way, forcing the distance between the two to remain constant. When the tether is cut, does the galaxy join up with the Hubble flow and start to recede due to the expansion of the universe? The intuition that says that objects suffer from a temptation to be swept up in the expansion of the universe will lead to an affirmative answer, but the truth is the reverse: unless there is a large cosmological constant and the galaxy’s distance is comparable to the Hubble length, the galaxy falls toward us. Similarly, it is commonly believed that the Solar System has a very slight tendency to expand due to the Hubble expansion (although this tendency is generally thought to be negligible in practice). Again, explicit calculation shows this belief not to be correct. The tendency to expand due to the stretching of space is nonexistent, not merely negligible.

(3) On The Relativity of Redshifts: Does Space Really "Expand"? The least technical of the batch, this article is also focused on the interpretation of the cosmological redshift. It includes the choice paragraph:

> While it may seem that railing against the concept of expanding space is somewhat petty, it is actually important to set the scene straight, especially for novices in cosmology. One of the important aspects in growing as a physicist is to develop an intuition, an intuition that can guide you on what to expect from the complex equation under your fingers. But if you [are] assuming that expanding space is something physical, something like a river carrying distant observers along as the universe expands, the consequence of this when considering the motions of objects in the universe will lead to radically incorrect results.

No. Space doesn;t expand within galaxies, it expands between galaxies, in the empty spaces.

It's not known if space is a physical object. We do not have the ability to see it expand at a microscopic level. (And also we have no way to get outside the galaxy.)

That sounds plausible. So to further and solidify my understanding, space itself is not expanding, just that physical entities (e.g. galaxies and therelike) are moving apart carried by their initial momentum.
But what I don't quite understand is the notion that this expansion (or motion) seems to accelarate relatively to each other, to a point where distant objects become unreachable for us even with we could travel at the speed of light. Or am I mixing things up here?

As a physicist who works nowhere near this field, this was a really enjoyable read. My first instinct was to ask about the cosmological redshift, which you addressed. But one thing I was concerned about that you didn't address was the accelerating expansion of spacetime.

Saul Perlmutter won the Nobel prize by using supernova standard candles to prove that the expansion of the universe was accelerating. Doesn't this indicate that the expansion of the universe is a real physical phenomenon - and that it certainly isn't just because of things moving generally apart from one another?

And what about all this discussion about the cosmological constant and vacuum energy (I think this is the same thing as my first question)? If the universe itself isn't expanding, why do we discuss a constant energy density throughout space that causes... an expansion.

Another question: it is often said in, frankly mostly youtube videos, that in the very late universe "the expansion of the universe will rip apart atoms and eventually protons." So is this just completely wrong? I see the statement in your (2) reference saying that atoms do not, in fact have to "resist the temptation” to expand.

> That sounds plausible. So to further and solidify my understanding, space itself is not expanding, just that physical entities (e.g. galaxies and therelike) are moving apart carried by their initial momentum.

Exactly.

> But what I don't quite understand is the notion that this expansion (or motion) seems to accelerate relatively to each other, to a point where distant objects become unreachable for us even with we could travel at the speed of light. Or am I mixing things up here?

Dark energy induces gravitational repulsion, which accelerates the expansion of the universe and also creates a cosmological event horizon. Indeed the mathematics are very similar to that of a black hole, but inverted, so that whereas things too close to a black hole cannot escape, with dark energy, things that are too distant (with respect to any observer) cannot return. (When thinking about unreachable distant objects, it is we who have become too distant from the object.)

Within the framework of general relativity, dark energy induces gravitational repulsion, which essentially accelerates everything away from everything else. That means it accelerates cosmic expansion.

While this repulsion is sometimes framed as a consequence of accelerating expansion, it doesn't really make sense to put the causation in that direction. For example, in Einstein's static universe, there is repulsion, even though the universe is static (because the repulsion balances matter's attractive gravity). It's really just gravitational repulsion arising from the energy density of dark energy (or the cosmological constant).

That happens only if dark energy is phantom energy, which is not really supported by observations or theory, but can't be definitely ruled out either. Essentially what happens is that in these models, the pressure of the dark energy fluid is sufficiently negative that expansion raises its energy density. With higher energy density, its gravitational repulsion becomes stronger. Eventually the repulsion becomes strong enough to separate atoms.

> The tendency to expand due to the stretching of space is nonexistent, not merely negligible.

Note that this claim is at odds with one of the papers that is cited in support (ref. 19 specifically). The final sentence of arXiv:astro-ph/9803097 reads:

> As a conclusion, it is reasonable to assume that the expansion of the universe affects all scales, but the magnitude of the effect is essentially negligible for local systems, even at the scale of galactic clusters.

Odd, I'm not sure why they cite that there. But the error made in the Cooperstock et al. article is pretty elementary, in any event. By starting with the FLRW metric for an Einstein-de Sitter universe, they assume from the outset that matter is homogeneously distributed everywhere at the critical density. The force that they claim arises from the expansion of the universe is really just the gravitational influence of this matter.

Is this askscience FAQ answer about "what is the universe expanding into" incorrect? It's saying that the distance between two "otherwise stationary" points will continue to increase. And that our "cosmic ruler" grows over time. To a non-cosmologist like me that sounds like the expert is saying space itself is expanding

I might be wrong but you can think of it like this: Between us and andromeda there is 'x' amount of dark energy repulsion. Between andromeda and the next galaxy beyond that there is also 'x' amount of dark energy repulsion. And so on. So between us and some galaxy thats 100 times farther away than andromeda is, there will be 100x amounts of dark energy repulsion.

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Bravo, very thorough and informative answer. Thank you for taking the time to make it so.

I feel like the description that it’s just like particles rushing away from each other doesn’t address the detail that the further the two galaxies in space are.. the greater their “expansion” rate is. That detail wouldn’t apply to particles moving away from each other

Is there any functional difference between the misconception you speak of in your initial post and the reality you describe above in terms of the physical outcome?

For example, if “space was expanding” except for things that are close enough overpower it with gravity, how would that result be different from dark energy creating a repulsive force except for things that are close enough to overpower it with gravity?

Also, how can galaxies be “carried by their initial momentum” as you confirmed above AND all be moving away from one another at the same time. Maybe I’m misunderstanding something but that doesn’t really make sense. The only way all galaxies that are not locally bound to one another could be moving away from one another is if that space between them is somehow expanding, similar to the “dots on the surface of a balloon” metaphor that is often used. If we instead imagine an “initial momentum” scenario, it suggests a single point of origin in space, similar to an explosion. But in the case of an explosion, there is a center source, which the universe doesn’t appear to have. Also, the red-shifting caused by an explosion would not be so uniform, but have many items moving away at much faster speeds than others relative to the observer.

> For example, if “space was expanding” except for things that are close enough overpower it with gravity, how would that result be different from dark energy creating a repulsive force except for things that are close enough to overpower it with gravity?

The main problem is that dark energy's repulsion has no intrinsic link to the global expansion of the universe. For example, as I noted in another comment, in Einstein's static universe (in which matter's attraction balances dark energy's repulsion), there is a repulsive force even though the universe is not expanding.

More generally, the repulsion from dark energy has no link to the cosmic expansion rate at a given instant. It does connect to the rate of change of the cosmic expansion rate (i.e. the acceleration), but this link is only partial, since dark energy is only one of the factors controlling the rate of cosmic acceleration (the other main one being matter, which decelerates expansion).

> Also, how can galaxies be “carried by their initial momentum” as you confirmed above AND all be moving away from one another at the same time. Maybe I’m misunderstanding something but that doesn’t really make sense. The only way all galaxies that are not locally bound to one another could be moving away from one another is if that space between them is somehow expanding, similar to the “dots on the surface of a balloon” metaphor that is often used. If we instead imagine an “initial momentum” scenario, it suggests a single point of origin in space, similar to an explosion. But in the case of an explosion, there is a center source, which the universe doesn’t appear to have.

The universe can originate from a single point in spacetime while still having no center in space. Due to the principle of relativity, any observer departing from that point has an equally good reference frame, so there is no way to decide that one observer is better than another.

(You could still suggest defining the center in terms of "distance from the edge". There doesn't have to be an edge, though.)

> Also, the red-shifting caused by an explosion would not be so uniform, but have many items moving away at much faster speeds than others relative to the observer.

That's not a fundamental limitation, it's just intuition from the explosions you know. The initial "explosion" doesn't have to be messy (for example if it arose from inflation). Also note that in an expanding system, velocities self-sort because if an object is moving rapidly with respect to the material near it, it's not going to stay near that material. Instead it will gradually end up near material moving at the same speed. (This effect is essentially the cosmological redshift applied to massive particles.)

Sure it would. Imagine that a bunch of particles all explode outward from a point at different speeds. The ones moving fastest will end up farthest, and you automatically end up with a picture where recession speed is proportional to distance.

It's fine to view space as expanding, since again, that represents a convenient coordinate choice. I use it frequently in calculations. The key point is just that this "expanding space" doesn't have physical consequences.

It's like how two people walking due north from the south pole will gradually separate from each other despite walking in the same cardinal direction, but the process of walking north doesn't induce an expansion force on your body.

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Which implies that your top-level comment is incorrect. There is a force acting at small scales, due to the cosmological constant, there is a tendency to expand that you need to counteract via gravity for things to become static.

Note that the Weinberg interview you quote is from 1993. This was years before the discovery of the accelerated expansion of the universe. At the time it was thought that the expansion of the universe was purely inertial, but we know better now, and you should stop spreading obsolete information.

The repulsive force acting at small scales is not linked to the cosmic expansion rate, as detailed in other replies. It is highly misleading to attribute it to the "expansion of space". It's just gravitational repulsion arising from the (stress-)energy density of dark energy.

Of course it is linked to the cosmic expansion rate, it is the very thing that is making the expansion rate accelerate!

Dark energy's gravity accelerates cosmic expansion. Dark energy also induces small-scale gravitational repulsion. However, we cannot say that cosmic expansion induces small-scale gravitational repulsion, because the two are not directly linked.

That is the claim in the top-level comment: that cosmic expansion does not have a local dynamical influence. This claim remains correct.

Of course cosmic expansion does not induce small-scale gravitational repulsion, it's the other way around. It's incomprehensible how can you say that they are not directly linked.

I think you are focussing too much on correcting the misconception that the inertial expansion of the universe is somehow a force pulling things apart, so much that you are ignoring the fact that the cosmological constant is a force pulling things apart that in fact causes the cosmic expansion to accelerate.

I'm addressing expansion of space because that's the topic of the question. I am confused as to why you think I should answer a different question.

(Regardless, it would seem to me that the appropriate course for you would be to make a separate answer, rather than to falsely claim that the existing answer is incorrect!)

Because you are so emphatic in your answer that expansion is not a force that one gets the impression that no such force exists. For example, you quote > You shouldn’t think of galaxies as being pulled apart by some kind of expanding space

and > there is no local effect on particle dynamics from the global expansion of the universe: the tendency to separate is a kinematic initial condition, and once this is removed, all memory of the expansion is lost.

While both sentences are technically correct, a lay person will incorrectly conclude that no local repulsive force exists. I don't think this is good science communication.

That's a fair suggestion. I'll make sure to include mention of dark energy next time.

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