How does the expansion of the universe work?

[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?

 

[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.

 

[Drakkith]

If the universe is infinite, how does someone calculate something infinite getting bigger? From a reference point? Is the rate of expansion the same for every point in the space?

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.

 

[EdColider]

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.

Thank You

 

[EdColider]

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.

Thank You

 

[phinds]

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

 

[EdColider]

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

Cool. I've never heard about it before.

 

[EdColider]

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

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.

 

[phinds]

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.

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.

 

[EdColider]

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.

Thank You

 

[EdColider]

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.

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

 

[Drakkith]

What I can't understand is how does someone calculate the variation of something infinity.

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

 

[Orodruin]

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)

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.

 

[PeterDonis]

in the case of the expanding universe, the stars are not actually moving.

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

They are getting further apart due to the expansion of space.

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.

 

[Orodruin]

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

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.

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.

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.

 

[PeterDonis]

you know as well as I do that when no frame is specified in cosmology, we are usually referring to the comoving coordinates

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.

what would you use instead in this case?

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.

 

[Orodruin]

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.

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.

 

[Jorrie]

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

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.

 

[PeterDonis]

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

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.

 

[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.

Langauge like that might or might not help newcomers.

 

[rede96]

Langauge like that might or might not help newcomers.

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. :)

 

[Jorrie]

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'.

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 anyone theory.

 

[rede96]

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.

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

 

[Orodruin]

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

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.

 

[Jorrie]

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

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?

 

[rede96]

I presume that you understand how the expansion equations work?

I sort of have a basic layman's understanding from things I have read and watched. In particular Leonard Susskind's lectures on cosmology, as well as a various other things. So my knowledge is very basic.

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.

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

As I understand it, GR doesn't predict expansion, it predicts the universe will contract under gravity. The cosmological constant (Lambda) was added to keep the universe static. So if it is adjusted to >0, then the model describes an expanding universe sure. But it is just a model that describes how the universe is expanding, not what caused expansion in the first place.

Again, from my limited understanding, I thought the universe initially expanded very rapidly prior to the big bang, (Inflation) due to the vacuum energy being many orders of magnitudes bigger than it is today. So this caused to universe to double in size about every 10^-32 seconds. When the vacuum energy suddenly collapsed, matter was formed and the universe heated up very rapidly (which I understand is the big bang) and the energy density dropped to be somewhere near the value it is today. So in orders of magnitude, the universe is about the same size as it was just after the initial inflation, doubling in size about every 10 billion years.

Now as I understand it, Dark Energy, Vacuum Energy, Cosmological Constant... they are all the same thing. So it is the same 'energy' that was responsible for inflation that is now responsible for the acceleration of the universe. So we couldn't have this acceleration without 'Dark Energy' (Vacuum energy)

Hence why I asked what theory of expansion there was without dark energy, because without dark energy there would have been no expansion at all.

 

[Jorrie]

As I understand it, GR doesn't predict expansion, it predicts the universe will contract under gravity.

No, GR predicts that the cosmos must either expand or contract - it can never be static for a length of time. The cosmological constant cannot make it stably static anyway. Einstein did attempt that by adjusting the value of Lambda, but it is easy to prove that such a state is not stable and would have quickly tipped over to either contraction or expansion.

I'm not too knowledgeable on inflation, because it is not part of the ΛCDM cosmological model, but AFAIK, inflation is not driven by 'dark energy'. There are many possible sources under investigation. The other fact that you seem to have missed is that 'dark energy', 'vacuum energy' and the 'cosmological constant' are not equivalent. I'm short on time at the moment, so please google the terms and see if you can understand the differences.

 

[PeterDonis]

without dark energy there would have been no expansion

No, without dark energy there would not be accelerated expansion today. But there can be expansion without accelerated expansion. They're not the same thing.

 

[rede96]

The other fact that you seem to have missed is that 'dark energy', 'vacuum energy' and the 'cosmological constant' are not equivalent.

Yes, sure. Sorry I didn't explain myself properly. I understand the cosmological constant is a parameter in GR, Dark energy is referred to as responsible for the accelerating rate of expansion and Vacuum energy is implied to exist through quantum field theory. So in that respect they are not exactly the same but they all refer to some 'energy' that has an effect on expansion.

I know Vacuum energy is thought to be too many orders of magnitude bigger for it to be responsible for dark energy, but there is still some 'energy' that permeates all of space. The part that seems to confuse me is if the energy responsible for accelerating expansion the same energy that was responsible for Inflation? It must have present since before the big bang. By the way, as I understand it, the big bang is not responsible for the early expansion, that came from inflation.

No, without dark energy there would not be accelerated expansion today. But there can be expansion without accelerated expansion. They're not the same thing.

Again, I am confused about how there could be expansion without dark energy? If you have time, could you explain that please. (In English please, I don't speak Math very well! :D)

 

[Orodruin]

The part that seems to confuse me is if the energy responsible for accelerating expansion the same energy that was responsible for Inflation? It must have present since before the big bang. By the way, as I understand it, the big bang is not responsible for the early expansion, that came from inflation.

No, it is not the same. What caused inflation must have been much denser than today's dark energy. It must then have disappeared due to some sort of dynamics, which we can only speculate about. Although dynamic, it would have several properties in common with dark energy and it is entirely possible that whatever dark energy is also exhibits dynamical properties.

Again, I am confused about how there could be expansion without dark energy? If you have time, could you explain that please. (In English please, I don't speak Math very well! :D)

This is similar to asking "can you explain the color blue? I am blind". If you are not willing to learn the math, you will essentially have to take it on faith from those who do know it. It is similar to the fact that if you throw something up, it can have a velocity in the up direction even thouh the gravitational force pulls it down.

 

[phinds]

Again, I am confused about how there could be expansion without dark energy? If you have time, could you explain that please. (In English please, I don't speak Math very well! :D)

Expansion now is simply a continuation of the original expansion (not inflation which is different as Orodruin has pointed out). Dark Energy causes the ACCELERATION of that expansion, as Peter has already pointed out.

I suggest you read the article linked to in my signature. I explain about inflation/expansion/acceleration-of-expansion.

 

[Jorrie]

By the way, as I understand it, the big bang is not responsible for the early expansion, that came from inflation.

In my opinion, the 'Big Bang' as it is used today is simply a catch-all for whatever preceded the present expansion dynamics (which proceeds according to the Friedmann solution to the GR equations). It could have been 'standard inflation', or a type of bounce, or even a relatively smooth, but dense transition from an earlier contraction phase, without a 'Bang'. Nobody quite knows, but it is the subject of intense study and observation.

BTW, 'dark energy' could conceivably be just the cosmological constant, interpreted as a constant inherent spacetime curvature that was left over after inflation (or whatever condition started the later expansion phase). It is still the simplest interpretation that seems to fit the bulk of observational data. There are some areas of so-called "tension" between data and the constant Lambda, but it is also the subject of intense study.

 

[rede96]

No, it is not the same. What caused inflation must have been much denser than today's dark energy. It must then have disappeared due to some sort of dynamics, which we can only speculate about. Although dynamic, it would have several properties in common with dark energy and it is entirely possible that whatever dark energy is also exhibits dynamical properties.

Ah, ok, thanks. I think I must of misunderstood some of the lectures on this bit, as it seemed to imply dark energy was part of the left over energy that caused inflation. But I'll go through it again.

This is similar to asking "can you explain the color blue? I am blind". If you are not willing to learn the math, you will essentially have to take it on faith from those who do know it.

Yes of course, I understand I'd have to take things on faith without learning the math, which is fine. And I do try and learn what I can. But If I want to work in a foreign country then yes I'd need to learn the language but if I just want to find out more about it, then English is often good enough :D

Expansion now is simply a continuation of the original expansion (not inflation which is different as Orodruin has pointed out).

Original expansion? What caused the original expansion? It seems like you are implying that there was inflation, then the universe stopped growing, then expansion started? Could you clarify what you mean please.

In my opinion, the 'Big Bang' as it is used today is simply a catch-all for whatever preceded the present expansion dynamics (which proceeds according to the Friedmann solution to the GR equations). It could have been 'standard inflation', or a type of bounce, or even a relatively smooth, but dense transition from an earlier contraction phase, without a 'Bang'. Nobody quite knows, but it is the subject of intense study and observation.

Ok, thanks. That is sort of how I understood it. I guess I just concluded at some point that expansion was linked to inflation, so were part of the same thing.

BTW, 'dark energy' could conceivably be just the cosmological constant, interpreted as a constant inherent spacetime curvature that was left over after inflation (or whatever condition started the later expansion phase). It is still the simplest interpretation that seems to fit the bulk of observational data. There are some areas of so-called "tension" between data and the constant Lambda, but it is also the subject of intense study.

In the Leonard Susskind lectors he often refers to Dark energy and the cosmological constant as being the same thing.

 

[phinds]

Original expansion? What caused the original expansion? It seems like you are implying that there was inflation, then the universe stopped growing, then expansion started? Could you clarify what you mean please.

I can't even remotely see how you infer that from what I said. Where did I even come close to implying that there was ever any stopping in the expansion? For the causes of the original expansion/inflation you'll have to ask someone else. All I'm saying is that the universe was expanding from the beginning and it has never stopped. Without Dark Energy, it was expected, up until the late 1990's, to eventually slow down, reverse, and end in a big crunch. Dark Energy had nothing to do with the original expansion.and still doesn't, but it has everything to do with why the Big Crunch concept has been abandoned by mainstream cosmology.

 

[Jorrie]

Ok, thanks. That is sort of how I understood it. I guess I just concluded at some point that expansion was linked to inflation, so were part of the same thing.

When I first studied modern cosmology (around Y2K), I made the following plot in an attempt to understand the "whole of expansion". I used 'r' to depict the radius evolution of the presently observable universe, with r_P and t_P the Planck radius and time respectively.

It is more or less correct for the simplest form of inflation, where Lambda was at a constant large value until end of inflation. Thereafter it is radiation dominated until ~10⁵ years, matter dominated until ~10¹⁰ years and thereafter Lambda dominated.

This is not unlike the nice 'trumpet' expansion pictures we often see in articles.

 

[phinds]

When I first studied modern cosmology (around Y2K), I made the following plot in an attempt to understand the "whole of expansion"...

Nicely done. Thanks for posting.

 

[nikkkom]

I think we need a FAQ (pinned post?) which explains all this in some very understandable-for-layman way.

Here's my attempt.

The "ordinary Big Bang and expansion" (no inflation, no dark energy):
Einstein's GR allows a solution (FLRW metric) where an empty Universe expands. Imagine that you have particles (say, hydrogen atoms) in a cubic grid with exactly 1 light year between nearest particles. (We assume that they weigh so little that this Universe is essentially behaves as if it is empty). And after each second distance between each particle increases by 1 meter. Not because they move, but because space "grows". That's that solution.

Even though empty Universe is expanding without slowing (distance between test particles grow by exactly one meter per sec), note that if you look back into the past of this Universe there were times when test particles were much closer together - say, only a billion km apart - and they moved away at exactly one meter per sec too. It's clear there was a moment where they had to be zero meters apart. That's "Big Bang" moment. The moment itself is problematic (singularity!), but any moment after that is not. For example, one microsecond after it test particles were 1 microsecond apart. It's a bit curious that in this scenario expansion seems to be very fast at first ("density" of test particles falls very quickly), and millions of years later, it looks very gradual, but expansion speed is in fact constant!

Now, if you use GR with Λ > 0, the picture changes. Grid of test particles grows not by exactly one meter per sec! Now it grows faster with time. If Λ is very small, at first speedup is not noticeable, but later it will be: test particles will not only move away from each other, they will seemingly do that faster with time.

That's one possibility what dark energy is - maybe it's just Λ. However GR with Λ = 0 but with some other field permeating all space and having appropriate property (negative pressure) will have exactly the same behavior.

How presence of matter changes this? FLRW metric with homogeneous distribution of matter will expand too, but expansion will slow down. (Heuristically, "matter will attract itself and try to shrink the Universe"). If there are lots of matter, expansion speed can even go to zero and start going backwards. Between "too little matter, eternal expansion with nonzero speed" and "too much matter, expansion stops" there is a borderline case where expansion never stops, but its speed falls ever lower, tending to zero with time, but never reaching it (that's "critical density Universe"). This all was about "normal" matter, with positive pressure. With "negative pressure matter" it's effect is opposite - this was already describe in the previous paragraph - that's "dark energy".

And finally, what if dark energy field is variable (e.g. it has several possible stable values) and one of these value is large (or there may be several such fields)? Alternatively, what if Λ can not only be larger than zero, but can be VERY MUCH larger than zero? Nothing unusual will happen, the Universe will behave as described above: grid of test particles grows faster with time. Very, very much faster. That's inflation. (If you have a separate "big dark energy field" for it, that's "inflaton field").

If you have inflationary Universe, even with matter, it expands astoundingly quickly, essentially becoming empty. And if then suddenly Λ (or dark energy) goes down to a very small value, you get an empty symmetrical flat expanding Universe. If "Λ going down" releases energy (in a form of appearance of new particles everywhere), you get a NON-empty symmetrical flat expanding Universe.

 

[Chronos]

The cosmological constant is a special case of dark energy. Specifically it is the case where w=-1. For discussion, see https://ned.ipac.caltech.edu/level5/March04/Carroll/Carroll4.html

 

[Jorrie]

It is a good starting point, nikkkom, but I spot a few terminology issues:

And after each second distance between each particle increases by 1 meter. Not because they move, but because space "grows". That's that solution.

The problem with "that solution" may be the "growing" of space. It is really only distances between comoving observers that grows.

For example, one microsecond after it test particles were 1 microsecond apart. It's a bit curious that in this scenario expansion seems to be very fast at first ("density" of test particles falls very quickly), and millions of years later, it looks very gradual, but expansion speed is in fact constant!

I think on this forum we have concluded that we should rather speak of expansion rate H(t) (not expansion speed) as a constant during exponential growth of distances (like a constant % per unit time). Marcus had a lengthy thread on that.

 

[nikkkom]

It is a good starting point, nikkkom, but I spot a few terminology issues:

The problem with "that solution" may be the "growing" of space. It is really only distances between comoving observers that grows.

For a layman explanation, you need to emphasis that it is something different from "ordinary" increase of distance due to observers moving relative to each other. In Minkowski space (i.e. no space expansion), you can't have an infinite cubic grid of observers 1 l.y. apart, moving so that grid increases by 1 m/s - you'll need some observers to move faster than light, which is not allowed. Hence, I choose different wording, not "distance is growing" but "space is growing".

 

[Jorrie]

... Hence, I choose different wording, not "distance is growing" but "space is growing".

I'm not sure if these words are compatible with metric expansion, whereby the scale of space itself changes, which I think is the concept that we should convey. How to do this using common words is a difficulty that all layman's treatments face.

Maybe we can say that each infinitesimal volume of space is 'growing' as scale increases and thus the proper distance between comoving observers increases?

 

[Orodruin]

I think that in the end, any word in English is going to be open to interpretations and misunderstandings. Mainly because English has not evolved with understanding of metric expansion as a relevant issue. After all, the word "expansion" was chosen and not because physicists want to give people the wrong idea, but likely because it was what gave the best English approximation. To really understand what is going on you will need at least some amount of math.

 

[rede96]

The problem with "that solution" may be the "growing" of space. It is really only distances between comoving observers that grows.

Just to highlight this one point, as I think this is something that causes a lot of, if not the most confusion for the layman. Is it just distance between commoving observers that grows or is there some other 'property' of empty space that is growing too? Or at least not diluting.

I read often that the reason galaxies separated by large cosmological distances can move apart with speeds much greater than c is because it is the space 'growing' between them that causes them to separate and not them moving through space relative to each other.

This in layman's language would seem to contradict your statement that it is really only distances between commoving observers that grows, as that implies that it is possible for some 'force' to eventually be separating them at speeds greater than 2c.

So I think a little more may be needed than just 'distances growing' but I'm just not sure what!EDIT: Sorry, didn't see this before posting.

I'm not sure if these words are compatible with metric expansion, whereby the scale of space itself changes, which I think is the concept that we should convey. How to do this using common words is a difficulty that all layman's treatments face.

Maybe we can say that each infinitesimal volume of space is 'growing' as scale increases and thus the proper distance between comoving observers increases?

 

[Jorrie]

This in layman's language would seem to contradict your statement that it is really only distances between commoving observers that grows, as that implies that it is possible for some 'force' to eventually be separating them at speeds greater than 2c.

Metric expansion does exactly that (in the cosmos we live in, at least). The most remote observed regions of space (where the presently observed CMB radiation originated) recede from us at over 3c (calculated from the redshift of over 1000). In other words, if there happened to be a comoving object there, its recession speed (or rather recession rate) in terms of dD/dt would have exceeded 3c, where D is the proper distance to the object and t is cosmic time. But, there is no 'force' necessary to do that - it is essentially spacetime curvature that causes the recession.

The challenge is to somehow convey this to novices without creating false perceptions. "Expanding space", "growing space", "speed of expansion", "increasing distance between comoving observers", etc. are all conducive to false perceptions. As Orodruin said, maybe there is no way to convey it in English without opening up an avenue for incorrect interpretations. Analogies like the balloon help, but then we all know about the wrong perceptions that they can cause.

To me it seems that beginners always have a lot of "why questions", while science can only answer the "what questions".

 

[PeterDonis]

In Minkowski space (i.e. no space expansion), you can't have an infinite cubic grid of observers 1 l.y. apart, moving so that grid increases by 1 m/s - you'll need some observers to move faster than light, which is not allowed.

Yes, you can, if you define "space" differently. In the "empty universe" FRW model, which is just a different coordinate chart on Minkowski spacetime, "comoving" observers are a infinite grid that increases in size at a constant rate. But the "space" described by the grid is not Euclidean 3-space; it's hyperbolic 3-space. (If you look at how this "grid" appears in ordinary Minkowski coordinates, the surfaces of constant "comoving time", if we just look at one spatial dimension, are hyperbolas, not straight lines.)

The point of all this is that "space" is coordinate-dependent; there is no absolute definition of "space". So there is no absolute definition of terms like "space expansion" either; you have to specify what coordinates you are using, and the same spacetime can appear to have "space expansion" in one coordinate chart but not in another.

 

[nikkkom]

Will that be possible in a non-empty Universe (i.e. to model ours)?

 

[PeterDonis]

Will that be possible in a non-empty Universe (i.e. to model ours)?

Sure, although the "non-expanding" coordinate chart won't be a simple one like the Minkowski chart, and the worldlines which are "at rest" in the "non-expanding" coordinates won't be inertial, as they are in Minkowski spacetime.

 

[rede96]

In other words, if there happened to be a comoving object there, its recession speed (or rather recession rate) in terms of dD/dt would have exceeded 3c, where D is the proper distance to the object and t is cosmic time. But, there is no 'force' necessary to do that - it is essentially spacetime curvature that causes the recession.

So just to check my understanding, is the following correct?

Dark energy does exert a force. What I mean by that is that all matter (or the space between particles) very slightly expands until it reaches a new state of equilibrium due to dark energy. So the universe may 'expand' due to the curvature of spacetime (although we don't know for sure if space is flat or not) but that expansion is accelerated by dark energy. Moreover the amount dark energy density doesn't dilute as space expands. If there were no dark energy it is most likely the universe would have collapsed on itself due to gravity. There was an initial period of inflation that was caused by some 'energy' field, but this energy field is not dark matter as all that energy was dissipated during inflation, which led to re-heating (big bang) and the first matter being formed. Also spacetime curvature in isolation would not have led to distance galaxies receding faster than C, so dark energy is responsible for that.

 

[nikkkom]

Dark energy does exert a force. What I mean by that is that all matter (or the space between particles) very slightly expands

yes.

until it reaches a new state of equilibrium due to dark energy.

no. It will expand, faster, and faster, forever. No equilibrium.

So the universe may 'expand' due to the curvature of spacetime

Wrong terminology. space expansion IS a form of curved spacetime - non-curved one would not expand or contract.

(although we don't know for sure if space is flat or not)

We know for sure that space*time* is curved (we see it expanding). What we don't know is whether its purely spatial slices are flat or not. It may be so that space (not space*time*) at a fixed comoving time is flat.

Moreover the amount dark energy density doesn't dilute as space expands.

In many models, yes (If dark energy is Lambda, if dark energy is vacuum energy). There are more contrived models where dark energy is a bona fide quantum field and thus can vary in time and space.

There was an initial period of inflation that was caused by some 'energy' field, but this energy field is not dark matter as all that energy was dissipated during inflation, which led to re-heating (big bang) and the first matter being formed.

Inflation is qualitatively the same as today's accelerated expansion - IOW, it also needs "dark energy". The difference is in magnitude. In present Universe, it would take many trillions of years for us to see all other superclusters except Laniakea disappear from the sky due to accelerating expansion. During inflation, that was happening in something like 10^-32 second. IOW: "inflationary dark energy field" had very large value.

 

[rede96]

Thanks for the reply, just a couple of comments:

no. It will expand, faster, and faster, forever. No equilibrium.

I think I must of worded that part wrong, I didn't mean that 'space' reaches an equilibrium, I meant that there is pressure from dark energy that acts in a very minute way on all mater which, causing it to expand very slightly. So a meter stick is just slightly longer due to dark energy than it would be without it. I am sure that part is correct, well at least according to everything I have read on it.

Wrong terminology. space expansion IS a form of curved spacetime - non-curved one would not expand or contract.

I need to read up a bit more on this, I get confused between what is physically space and what is spacetime. I think of it as spacetime being the 4-dimensonal structure our 3d universe is embedded in. But not sure if that is right or not. But other than the equations I am not sure how curved spacetime leads to expanding space.