# How does the expansion of the universe work?

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1. Dec 29, 2015

### EdColider

How does universe expansion work? I thought that the universe was infinite and the celestial corps were getting further distance from each other. If the universe is infinite, how does someone calculate something when infinity is getting bigger? From a reference point? Is the rate of expansion the same for every point in the space?

Last edited by a moderator: Jan 12, 2016
2. Dec 29, 2015

### andrewkirk

It isn't getting bigger. Things are just getting further apart.

Imagine the two-dimensional number plane with a star at every point with integer coordinates. Then imagine that, starting at time 0, the stars start moving so that the coordinates at time t of the star with coordinates (a,b) at time 0 will be ((t+1)a,(t+1)b). Then the stars are all getting further away from one another, even though the extent is infinite.
By the way, that formula is not the one that describes the actual way that galaxies in our universe move apart. It is a much simpler, somewhat unrealistic, formula that is intended solely to help you visualise this kind of thing.

3. Dec 29, 2015

### Drakkith

Staff Emeritus
When we talk about expansion we have to keep in mind that we are talking about how physical objects (and light) behave. What universal expansion means is that galaxies and galaxy clusters which are not bound strongly enough to each other through gravity will recede from each other over time. In other words, the distance between these unbound galaxy clusters will increase over time. This increase in distance follows a set of rules that can be naively described as an 'expansion' similar to how objects attached to a rubber band recede from each other as the rubber band is stretched (or a rubber sheet if you want to talk about expansion in 2 dimensions).

I want to emphasize that expansion is about the increasing distance between objects, not about space literally stretching like a rubber sheet. The rubber sheet is simply an analogy.

4. Dec 29, 2015

### EdColider

Thank You

5. Dec 29, 2015

### EdColider

Thank You

6. Dec 29, 2015

### phinds

@EdColider If you think infinity can't get bigger, google "Hilbert's Hotel".

7. Dec 29, 2015

### EdColider

Cool. I've never heard about it before.

8. Dec 29, 2015

### EdColider

I understand that we can always add 1 more item to a list.
What I can't understand is how does someone calculate the variation of something infinity.

9. Dec 29, 2015

### phinds

Your question is not clear. Do you mean "how much bigger does it get" ? If so, it is not a meaningful question, or put another way, it does not have a meaningful answer. Or, put another way, infinity plus 1 is exactly the same size as infinity so you can say it doesn't get any bigger at all.

10. Dec 29, 2015

### EdColider

Thank You

11. Dec 29, 2015

### EdColider

Sorry for the meaningful question. You really helped me out. :D

12. Dec 29, 2015

### Drakkith

Staff Emeritus
Look back at my post. Cosmologists don't typically deal with infinity, they deal with finite numbers, such as the distance between galaxies.

13. Dec 30, 2015

### Orodruin

Staff Emeritus
Note that in the case of the expanding universe, the stars are not actually moving. They are getting further apart due to the expansion of space. Compare with two ants holding on to a rubber band being stretched out.

14. Dec 30, 2015

### Staff: Mentor

"Moving" is relative. They are not moving relative to standard FRW coordinates, but they are moving relative to each other.

We should probably be careful about how we use the term "expansion of space", since in other threads people are being told that the inferences they are drawing from that phrase are wrong.

15. Dec 30, 2015

### Orodruin

Staff Emeritus
Obviously, but you know as well as I do that when no frame is specified in cosmology, we are usually referring to the comoving coordinates and I believe this is the standard assumption students will make if not told otherwise.

So what would you use instead in this case? It is what it is in comoving coordinates with cosmological time as the simultaneity convention. I think starting to get into these issues in an I thread is pulling it a bit too far.

16. Dec 30, 2015

### Staff: Mentor

Yes, I agree. But I'm still not sure that saying distant stars/galaxies are "not moving", meaning not moving relative to these coordinates, will avoid confusion. See below.

I would say that objects (or comoving objects if more precision is needed) are getting further apart (basically how andrewkirk started post #2). But that does imply that they are moving--saying they are "not moving", to me, implies that they are not getting further apart, which is why I think using the term "not moving" in this connection is likely to cause confusion.

17. Dec 31, 2015

### Orodruin

Staff Emeritus
Thats funny, I have the exact opposite experience, ie, that calling things "moving" is a source of widespread confusion such as ascribing cosmological redshift to the Doppler effect. Also, I think moving seems to imply changing spatial coordinates with time more than increasing distance.

Of course, it may be better to avoid using the word "moving" at all.

18. Dec 31, 2015

### Jorrie

I'm with you here. In co-moving coordinates, the only 'movement' will be peculiar movement. Cosmological redshift is then due to metric expansion, but the peculiar movement may have a Doppler effect that changes the observed redshift marginally.

19. Dec 31, 2015

### Staff: Mentor

That would be my preference, yes. Unless a spacetime is stationary, there is no way to construct a coordinate chart such that things are "moving" in one sense (nonzero coordinate velocity) iff they are moving in the other sense (nonzero observed redshift/blueshift of light signals between objects). And as soon as these two senses of "moving" are uncoupled, you have the potential for confusion, since our intuition says they should be coupled (more precisely, that we should always be able to choose coordinates so that they are coupled).

The problem is that it's really hard to describe, say, the properties of the FRW cosmological models in ordinary language without using the words "moving" or "expansion". We can do it with math, of course, but then we have to explain the physical meaning of the math, and again, that's really hard to do without using those two words.

20. Dec 31, 2015

### marcus

FWIW (my two cents) in the past I have said things like:
"Hubble law distance expansion is not like ordinary motion in the sense that nobody gets anywhere by it, everybody just becomes farther apart".

Nobody approaches a goal or destination by it, relative positions don't change, all the distances just increase by a fixed percentage per unit time.

It's like dots on an expanding sphere each staying fixed at the same latitude and longitude---not moving around in the ordinary sense but becoming farther apart.

This is allowed by spacetime curvature, the unintuitive thing at the heart of GR. GR says you have no right to expect distances NOT to change between relatively stationary objects---objects each of which is not moving in the space around it.

Language like that might or might not help newcomers.

21. Jan 1, 2016

### rede96

For me, what I find most confusing when trying to understand expansion is all the different interpretations of 'expansion'. For example, just what is expanding? Space?, Dark Energy?, Quantum fluctuation?, Something else? Just that fundamental question seems to cause a lot of confusion. It'd be great if someone could clear that one up.

Also, quite often people will say that it is the 'space' in-between galaxies that is 'growing' which 'pushes' the galaxies apart. For me personally, that is confusing, as just what it is that is 'growing'? How can 'space' physically exert a force on such massive bodies as clusters of galaxies in such a way to 'push' them apart?

My simple way of looking at this (which I accept might not be correct) is when we talk about 'expansion' we are really talking about matter (galaxies etc) that aren't bound by gravity, moving apart. The process that drives this is the vacuum energy (Dark Energy), which is a field that permeates all 'space'.

What I still get confused about is if the vacuum energy is 'expanding' or it is already present (from the initial inflation prior to re-heating) or if galaxies where the gravitational pull isn't strong enough to keep them together move apart because our universe is curved (like a sphere) and they are just 'falling' due to this curvature.

Anyway, just my 2 cents. :)

22. Jan 1, 2016

### Jorrie

The universe would have been expanding today even if there was no evidence of dark energy - just expanding at a lesser rate. So no, dark energy is not the reason for expansion.
Here are two charts, both for flat space expansion.
1) expansion with dark energy:

'a' is the scale factor and 'V_gen' is the recession rate of a galaxy that is presently at the Hubble radius (a 'generic recession rate').

2) Expansion without dark energy:

You can see that the two charts start off much the same, with 'decelerating expansion' and chart 1 shows late 'accelerating expansion', which we believe is caused by dark energy.

All that we can say with some certainty is that the universe presently expands because it expanded in the past. Exactly what started the expansion is not certain, because there are multiple theories and no conclusive evidence for any one theory.

23. Jan 2, 2016

### rede96

Just for clarification, could you tell me which theory predicts expansion without dark energy?

24. Jan 2, 2016

### Orodruin

Staff Emeritus
Expansion is part of any cosmological model based on the FRW metric in GR. The energy content of the universe then affects exactly how the expansion proceeds. Dark energy is only required for accelerated expansion.

25. Jan 2, 2016

### Jorrie

ΛCDM with Λ=0. With the values we measure today, Λ played a negligible role for the first few billion years, but for the last 5 billion years it is dominating the expansion dynamics. I presume that you understand how the expansion equations work?