How does the expansion of the universe work?

[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.

 

[Jorrie]

Dark energy does exert a force.

yes.

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.

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

I think there may be some confusion between two aspects of expansion here. Just like gravity is not a force in GR, dark energy is not a force, because comoving observers are all in free-fall. The only force is of tidal nature and matter with significant size experience stretch/squeeze forces that work against the forces that hold them together. For instance, the sizes of gravitationally bound clusters should stabilize at a size slightly larger than what it would have without dark energy.

When things are not gravitationally bound, then as nikkkom said, recession rates increase forever due to dark energy, with no equilibrium.

Whether expansion is seen as caused by spacetime curvature or if "space expansion IS a form of curved spacetime" maybe just a matter if interpretation. See : http://arxiv.org/abs/1111.6704 by Dag Østvang. The cosmological constant manifests itself as an intrinsic (constant) spacetime curvature.

 

[Orodruin]

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.

Then there remains two possibilities. Either everything you read was incorrect or your interpretation of it was. The accelerated expansion of the universe is not about the effect of the dark energy on the matter it contains, it is an effect of the dark energy on the space-time itself. Even if there was no matter in the universe, dark energy would lead to accelerated expansion.

A meter stick is a whole other issue, it is generally being held together by other forces which at short distances overcome expansion by a lot.

 

[nikkkom]

I need to read up a bit more on this, I get confused between what is physically space and what is spacetime.

Space is 3D, spacetime is 4-dimensional.

Imagine a "distorted" 3D grid - a grid where edges are not all of equal length. You can do a flat 2-dimensional cut through it at any angle.

If you discover that there is one particular cut direction which always gives you a 2D grid which is undistorted, then this 3D grid is distorted, but it has a "subspace" which is flat.

In current prevailing cosmological model, in comoving coordinates, a 3D "cut" through spacetime along the direction of constant time (IOW, Universe "frozen" at a constant comoving time everywhere) seems to be a flat (not curved) 3D space.

 

[rede96]

Then there remains two possibilities. Either everything you read was incorrect or your interpretation of it was.

Or my post was written in such a way that it was misunderstood. Or a combination of all three :)

The accelerated expansion of the universe is not about the effect of the dark energy on the matter it contains, it is an effect of the dark energy on the space-time itself. Even if there was no matter in the universe, dark energy would lead to accelerated expansion.

A meter stick is a whole other issue, it is generally being held together by other forces which at short distances overcome expansion by a lot.

Yes I understand this, I was simply making the point that dark energy does have a very small effect on matter. The forces that hold a meter stick together would obviously be far greater than this very small dark energy force, so the atoms are not forced apart, but dark energy still produces an effect on the meter stick.

 

[Orodruin]

The forces that hold a meter stick together would obviously be far greater than this very small dark energy force, but it still produces an effect on the meter stick.

Fine, but this effect is even smaller than the stick's self-gravity. Locally, the presence of the stick will be sufficient for space to not undergo accelerated expansion. Dark energy dominates at large scales only.

 

[rede96]

I think there may be some confusion between two aspects of expansion here. Just like gravity is not a force in GR, dark energy is not a force, because comoving observers are all in free-fall.

So would it be correct to say that due to GR, all co-moving observers which are not gravitationally bound are in free fall but just away from each other? Also that they accelerate away from each other just as a ball rolling down a hill accelerates? But it is dark energy that causes this 'rate' of acceleration to increase?

 

[Jorrie]

So would it be correct to say that due to GR, all co-moving observers which are not gravitationally bound are in free fall but just away from each other? Also that they accelerate away from each other just as a ball rolling down a hill accelerates? But it is dark energy that causes this 'rate' of acceleration to increase?

For the present epoch, essentially yes to all. But, like in all free-fall, it is only a coordinate acceleration, i.e. it depends on the coordinates chosen. E.g. in comoving coordinates, comoving galaxies do not move away from one another, so there can be no acceleration involved. It is thus not acceleration like when a rocket is firing, where we can observe proper acceleration, independent from coordinates choices. This is the type of acceleration that a simple accelerometer will show up.

 

[rede96]

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

Just out of interest I found the part in one of Leonard Susskind's lectures on cosmology where he refers to 'dark energy', 'vacuum energy' and the 'cosmological constant' all being the same thing and goes on to show why later in the lecture.

See the link below time index 33:30 and watch for about 30 seconds or so.


So do you know why he would refer to them as all being the same?

 

[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.

So, how about a pinned post based on the above "layman" description?

 

[Jorrie]

So do you know why he would refer to them as all being the same?

I'm not sure who the target audience was, but I think he kept it as simple as possible. In more advanced lectures it would be necessary to show that the cosmological constant is just a special case of dark energy (and the simplest interpretation, with w=-1). It is however possible to have w not exactly -1, which gives a dark energy density that changes over time (and possibly over space). It is called either 'quintessence' or 'phantom energy', depending on which side of -1 w sits. So exact equivalence cannot be generally assumed. Further, if you read https://en.wikipedia.org/wiki/Vacuum_catastrophe, you will also see an issue with the equivalence of vacuum energy and the cosmological constant.