Increase of dark energy with expansion of universe

[Vighnesh Nagpal]

Why does dark energy increase along with the expansion of the universe ( I'm not even sure it does but if it dosen't please correct me

 

[phinds]

It does and is well known to. It's not clear to me why it should, but the density of the "dark energy", whatever it is, remains constant as spacetime expands, so the total amount increases.

 

[Suraj M]

The dark energy density/concentration, remains a constant, ..as the universe expands, the dark energy also increases, to maintain it's concentration a constant
..also resulting in the accelerated expansion of the universe

 

[wabbit]

I don't know if there is a reason why dark energy density is - or should be - constant, but my (non expert) understanding of the reason it is usually assumed to be constant is that
- this is the only simplest form compatible with standard general relativity ;
- there is so far no observational evidence that forces cosmologists to abandon this assumption and go for something more general.
(Though alternative models do exist of course)

Edit : corrected, thanks PeterDonis

 

[PeterDonis]

this is the only form compatible with standard general relativity

Not really. It is the simplest form compatible with standard GR. A scalar field that varies with space and time but has an appropriate equation of state can also act like dark energy and is compatible with standard GR, but it's more complicated.

 

[wabbit]

Not really. It is the simplest form compatible with standard GR.

Thanks for the correction, edited that - I guess I was using "standard" in an unduly restrictive sense here.

 

[Chalnoth]

It does and is well known to. It's not clear to me why it should, but the density of the "dark energy", whatever it is, remains constant as spacetime expands, so the total amount increases.

I think the way you worded this is slightly confusing.

The density of dark energy remains constant, but everything else dilutes with the expansion. So over time, the dark energy makes up a larger fraction of the energy density. It doesn't increase: everything else just decreases.

 

[phinds]

I think the way you worded this is slightly confusing.

The density of dark energy remains constant, but everything else dilutes with the expansion. So over time, the dark energy makes up a larger fraction of the energy density. It doesn't increase: everything else just decreases.

Excellent correction. Thanks. I was going to add, and clearly should have, that the implication of (or really just another way of saying) "density of dark energy remains constant" is that it does not dilute within a given cosmologically large volume but the matter density does dilute.

 

[Vighnesh Nagpal]

oh ok. thanks guys!

 

[Uollises]

Never thought about it. But, does this dark energy have sources of..uhm..energy?)

 

[Chronos]

Im stuck on the Peter Donis explanation, what part of that you find incomprehensible?

 

[wabbit]

there is so far no observational evidence that forces cosmologists to abandon this assumption and go for something more general

To qualify this somewhat, the following paper (not completely sure if this is an acceptable source - will remove if not) assesses current observational constraints on dark energy anisotropy and inhomogeneity (and hints of a possible large scale dipole moment in dark energy) : Leandros Perivolaropoulos : Large Scale Cosmological Anomalies and Inhomogeneous Dark Energy

A wide range of large scale observations hint towards possible modifications on the standard cosmological model which is based on a homogeneous and isotropic universe with a small cosmological constant and matter. These observations, also known as "cosmic anomalies" include unexpected Cosmic Microwave Background perturbations on large angular scales, large dipolar peculiar velocity flows of galaxies ("bulk flows"), the measurement of inhomogenous values of the fine structure constant on cosmological scales ("alpha dipole") and other effects. The presence of the observational anomalies could either be a large statistical fluctuation in the context of {\lcdm} or it could indicate a non-trivial departure from the cosmological principle on Hubble scales. Such a departure is very much constrained by cosmological observations for matter. For dark energy however there are no significant observational constraints for Hubble scale inhomogeneities. In this brief review I discuss some of the theoretical models that can naturally lead to inhomogeneous dark energy, their observational constraints and their potential to explain the large scale cosmic anomalies.

 

[stevebd1]

Why does dark energy increase along with the expansion of the universe ( I'm not even sure it does but if it dosen't please correct me

I always thought this was a good overview of dark energy and the expanding universe-

http://preposterousuniverse.com/writings/skytel-mar05.pdf

 

[phinds]

I always thought this was a good overview of dark energy and the expanding universe-

http://preposterousuniverse.com/writings/skytel-mar05.pdf

Excellent reference. I really like Carroll; I think he's a good explainer. I have a "Teaching Company" set of 12 half-hour video lectures by him on "Dark Matter; Dark Energy" and they're excellent.

 

[marcus]

Why does dark energy increase along with the expansion of the universe ( I'm not even sure it does but if it dosen't please correct me

Vighnesh, I don't know of any scientific reason to think that "dark energy" actually arises from any form of energy. Some people think of it that way and others don't. All we observe is a small residual expansion rate that corresponds to a curvature constant that appears naturally on the lefthand side of the GR equation. In my experience it confuses people to think of it as some kind of energy---it's just a slight built-in spacetime curvature.

If you want to know the exact value in metric units, based on current observational measurements, it corresponds to a distance growth rate of 1.83 x 10^-18 per second. No mysterious "energy" needs to be involved.
The present fractional rate of distance growth (between things at cosmic rest, not gravitationally or otherwise bound together) is
2.20 x 10^-18 per second.
Each second, a large-scale distance distance grows by that small fraction of its length.

This fractional distance growth rate was much larger in the early universe and has been steadily declining ever since. It is expected to continue declining but not to reach zero. Instead it is expected to level off at 1.83 x 10^-18 per second.
Einstein included in his GR Equation the curvature constant Lambda which turns out to be three times the square of this rate.

If you google "general relativity" and get the Wikipedia article, you immediately see this Lambda in the standard form of the equation in the box on the right of the page.

Its value according to current estimates is about 10.0 x 10^-36 per second².
You can easily see how that works out: if you square 1.83 and multiply by 3 you get about 10, squaring 10^-18 gives 10^-36 and of course if you square "per second" you get "per second per second" or per second²

 

[Vighnesh Nagpal]

Hi. Thanks for your replies guys, really cleared it up for me :)

 

[Phynos]

This fractional distance growth rate was much larger in the early universe and has been steadily declining ever since. It is expected to continue declining but not to reach zero. Instead it is expected to level off at 1.83 x 10^-18 per second.

If the expansion is accelerating, why is this fractional distance growth rate decreasing? Doesn't that imply the acceleration is actually negative and that things are slowing down? Or am I misunderstanding what you're saying?

 

[phinds]

If the expansion is accelerating, why is this fractional distance growth rate decreasing? Doesn't that imply the acceleration is actually negative and that things are slowing down? Or am I misunderstanding what you're saying?

Think about this: You are going 100mph and you are accelerating at 20mph per hr, so in an hour you will be going 120 mph. At that point, your acceleration decreases to 19mph per hr, so in one more hour you will be going 139mph. Does that seem to you like "slowing down"?

 

[marcus]

If the expansion is accelerating, why is this fractional distance growth rate decreasing? Doesn't that imply the acceleration is actually negative and that things are slowing down? Or am I misunderstanding what you're saying?

that is a verbal problem, Phyrnos. the word "accelerating" is confusing people. the expansion rate has always been decreasing since the very early universe and according to the standard cosmic model (called LambdaColdDarkMatter, or LCDM) we expect it to continue decreasing, just not to get down to zero but to kind of level out at a longterm rate.

The big discovery in 1998 was that the longterm rate is not zero but is actually a small positive rate.

There are two ways they could have announced the 1998 result, which way sounds better to you?

===announcement one===
The present rate of distance growth is 1/144 of one percent per million years and we found that it is declining more slowly than was thought. Instead of gradually tailing off to zero it has been acting as if it is going to level out at 1/173 percent per million years.
==endquote==

The alternative would use scientific notation, to express these very small fractional growth rates, and the metric unit of time, the second. Each second the distance grows by a tiny tiny fraction of itself.

===announcement two===
The present rate of distance growth is 2.20 x 10^-18 per second and we found that it is declining more slowly than was thought. Instead of gradually tailing off to zero it has been acting as if it is going to level out at 1.83 x 10^-18 per second.
==endquote==

I don't like the word "acceleration" in this context because for most of us it has mental associations with driving a car. Driving a car is not a good metaphor for the pattern of cosmic distance growth described by Hubble Law. The analogies are weak, and awkward, and lead to confusion. A better analogy would be money in a savings account at the bank where the interest rate is gradually declining. If the fractional growth rate is declining GRADUALLY ENOUGH then the account can still grow each year by a larger dollar amount (because the principal is increasing). AFAICS the minute you use the word "acceleration" and start thinking about driving a car you have lost touch with the actual process occurring in nature.

 

[wabbit]

Oh you just corrected a deep misunderstanding of mine, thanks marcus. Plus that makes sense, I actually thought either statement true depending on what I was thinking about !

Back from deleting my post about this in another thread : )

I find it strange that we hear that expression "accelerating expansion" all the time when it is in fact not accelerating... This is just confusing, why make it so hard for us poor laymen to get even a broad understanding of what's going on !

Edit : Well I suppose it's accelerating in comparison to one that would be decreasing... kind of like my country's public spending is said to decrease whenever it increases less than previously expected : )

 

[marcus]

Wabbit, thanks for the encouraging comment. Now let's open the door a crack and let the word "accelerating" back in :grin: It's the idea of exponential growth, and quasi-exponential or near-exponential growth with a gradually declining rate.

I know I'm being ambiguous and wish-washy about this but having said that about the Hubble expansion rate H(t) which is indeed declining towards a longterm rate H_∞, there is also the SCALE FACTOR a(t) which is the size of a generic distance normalized to a(now) = 1.

Cosmologists need both H(t) and a(t), both those handles on distance growth are useful. As a fractional growth rate, H = a'/a
the small fraction of itself that a generic distance grows by, per unit time.

The Friedmann equation, as usually written, governs H. It tells you what H² is. and it shows how it is declining.

You could say that H, the "Hubble rate" is our main handle. But a(t) is in there too. And it is "accelerating" in a sense, because after about year 8 billion the second derivative of a(t) became positive. a'(t) has always been positive as long as the U has been expanding. But a'' was negative until around that time and then became positive. So there is a "scale factor" sense in which growth IS accelerating. think of a(t) as the size of the savings account. For a long time it grew by decreasing dollar amount each year because the bank was ramping down the interest rate so rapidly, but then the bank continued to decrease the rate, but more gradually, so it becomes quasi-exponential growth and the annual dollar amount increment grows.

the a(t) curve changes from convex to concave at an inflection point around year 8 billion. Some people use the notation R(t) for the scale factor.
Sorry to be adding to the confusion. But want to be fair to the scale factor, another important handle on the process.

 

[Phynos]

Think about this: You are going 100mph and you are accelerating at 20mph per hr, so in an hour you will be going 120 mph. At that point, your acceleration decreases to 19mph per hr, so in one more hour you will be going 139mph. Does that seem to you like "slowing down"?

No, I didn't mean the recession speed of far away galaxies was decreasing, but that the acceleration of that recession was decreasing. Poor wording on my part.

that is a verbal problem, Phyrnos. the word "accelerating" is confusing people. the expansion rate has always been decreasing since the very early universe and according to the standard cosmic model (called LambdaColdDarkMatter, or LCDM) we expect it to continue decreasing, just not to get down to zero but to kind of level out at a longterm rate.

The big discovery in 1998 was that the longterm rate is not zero but is actually a small positive rate.

I don't like the word "acceleration" in this context because for most of us it has mental associations with driving a car. Driving a car is not a good metaphor for the pattern of cosmic distance growth described by Hubble Law. The analogies are weak, and awkward, and lead to confusion. A better analogy would be money in a savings account at the bank where the interest rate is gradually declining. If the fractional growth rate is declining GRADUALLY ENOUGH then the account can still grow each year by a larger dollar amount (because the principal is increasing). AFAICS the minute you use the word "acceleration" and start thinking about driving a car you have lost touch with the actual process occurring in nature.

The second one makes sense to me, it just runs counter to what I have been previously told. Why would a astronomy professor use the term acceleration in this context in an introductory class if the word poses issues? Just because it's an introductory class?

I understand the distance growth rate, and I like it explained that way, but it seems to convert into the language of velocity and acceleration just fine unless I'm missing something? From what you explained above, it seems to me this is the situation:

(1) The distance between galaxies is increasing (radial velocity between distant galaxies is positive, positive being the direction away from us).
(2) This radial velocity is increasing (Positive acceleration caused by Dark Energy).
(3) However this acceleration is not increasing, but rather decreasing (AKA there is a negative jerk), and is presently creeping towards a minimum.

 

[marcus]

Human language is sometimes mysterious and once words get started it is hard to change them. Maybe someone can summarize this situation better than I. I want to be fair to the scale factor and its INFLECTION POINT which came about 5 billion or 6 billion years ago. You can see the inflection point around year 8 billion, that is around -5 or -6 on the time axis.

This is from a Lineweaver 2003 article. I'm a fan of Lineweaver. He's a world-class cosmologist and also good at presenting information. Even though it's old and in some ways out of date this Lineweaver article can be helpful to read. The title is "Inflation and the Cosmic Microwave Background".
Nowadays there are alternatives to inflation, maybe other things happened that achieved the same or similar observable effects. But so what? He is a good writer, and it is not all about inflation by a long shot. 90% about other stuff.

 

[wabbit]

And following this I checked other definitions for a few expressions we hear, hope I got this right:

Hubble scale = scale factor = a(t) or R(t), the characteristic scale of the universe, its size if finite.
Hubble parameter = Hubble rate = H(t) =$\dot a(t)\over a(t)$, the logarithmic growth rate of that scale.

Hubble constant = current value of the Hubble rate = H₀

Just need to be careful...

 

[wabbit]

Thanks marcus, actually your explanation makes perfect sense, I was just forgetting that "acceleration" mathematically can be an ambiguous term.

In fact it was even fine to think "accelerating" in one context and "slowing down" in another - but I needed to realize that:
- one is about the (increasing) growth rate of the scale factor,
- the other is about the Hubble rate, i.e. the (decreasing) logarithmic growth rate of the scale factor.

Thanks for clearing this up. Oh and nice chart you have here, just saw your last post - this wraps it up perfectly.

And I even get now that it isn't an evil conspiracy by physicists to keep the masses in the dark

 

[marcus]

And following this I checked other definitions for a few expressions we hear, hope I got this right:

Hubble scale = scale factor = a(t) or R(t), the characteristic scale of the universe, its size if finite.
Hubble parameter = Hubble rate = H(t) =$\dot a(t)\over a(t)$, the logarithmic growth rate of that scale.

Hubble constant = current value of the Hubble rate

Just need to be careful...

Perfect! That's probably how I should have started off.

And a simple way to write the (spatial flat) Friedmann equation that the whole cosmic model LCDM runs on is:

H² - H_∞² = const ρ

Where rho ρ is the combined energy density of radiation and matter (dark and ordinary)
and where "const" is a constant that converts energy density to squared growth rate
The constant that does this in the Friedmann equation is 8πG/(3c²).

 

[marcus]

Except for a pesky factor of c², Λ in the Einstein GR equation is equal to 3H_∞²

So that form of the Friedmann equation in the previous post could also be written (except for that c^2)

H² - Λ/3 = const ρ

Darn that c², it doesn't look so clean when I include it:
H² - Λc²/3 = const ρ

The conventional Lambda is in units of reciprocal area. In metric it would be m^-2
But relativists often switch between time and distance and sometimes Lambda is expressed in terms of seconds^-2. If that were understood, I wouldn't have to include the c².
It is there just to convert m^-2 to s^-2

 

[wabbit]

This is disappointing. Far too simple : )

 

[marcus]

You are always one hop ahead, Wabbit. Suppose we just cut the Gordian tangle by agreeing that Lamda is 10^-35 seconds^-2 as some relativists would have it. Then we get the clean form.

 

[wabbit]

Thanks but that's undeserved, I didn't notice a missing factor, was just impressed by the simplicity !

But anyway, c=1 so no big deal. (Other than, why do we move so fast in time and so desperately slowly in space? But that's for another thread, another day...)

 

[Phynos]

My comment was missed above.

I don't see how acceleration can be ambiguous. What's not clear about a changing rate of velocity?

If the scale factor is the factor by which the universe has increased, and this has a positive second derivative, then the expansion is indeed accelerating as I previously thought (As indicated by the graph you posted). As for the Hubble parameter, if that's the log of the growth rate, I don't care about that at the moment, which is what you seemed to be talking about before if I am not mistaken. When I first commented I cared about the properties of two points separated by a vast sea of space. How their distance varies over time.

 

[BillyT]

Is it true that:
(1) The total KE in stars, galaxies and even gas clouds is increasing despite mutual gravitational attraction? If yes, their total energy TE = KE + PE must be too.
If no, is their TE increasing, remaining constant or decreasing?
(2) Is the total of dark energy, DE, increasing with time? I think yes.
(3) Is conservation of energy law, thus false on scale of the universe?

 

[marcus]

Is it true that:

(3) Is conservation of energy law, ... false on scale of the universe?

Yes, it is false. Google "energy is not conserved in an expanding universe". You get a simple understandable blog post by Sean Carroll.
It is true regardless of "dark energy". We knew this before 1998 before "accelerated expansion" was noticed, back when the cosmological constant was assumed to be zero.

You are right that it is false, but this does not depend on your points (1) and (2).

 

[marcus]

BillyT, you run a risk of confusing your listeners or yourself if you think of the pattern of growing distances as if it were ordinary motion like what we are familiar with. Nobody GETS anywhere by it. No goal is approached relative positions are unchanged, nobody gets out of their own region that they were in and that light is traveling in. everybody just becomes farther apart.
It isn't governed by laws of KE that you are used to and that you invoke. It doesn't take energy to accelerate it. It is dynamic changing geometry, not ordinary motion. It is normal for the growth of distances to be faster than c. The distances to MOST of the galaxies that we can see with a telescope are increasing faster than c. The great majority are.

So the pattern of distance growth (expressed in Hubble Law) should not be thought of as ordinary familiar motion thru space that we are used to. It does not obey the same rules. Just some friendly advice---of course you can think of geometric expansion as motion thru space if you like, but it seems to work out better not to.

 

[marcus]

Wabbit, the constant 8 pi G/(3 c^2) in the Friedman equation converts energy density to a square growth rate. Something which in the metric system would have units seconds^-2 or "square hertz". hertz is metric for "per second" .
The google calculator really likes metric units, although you can get it to give answers in "per million years" etc etc. by specifying.

It's strange there is no other metric term for "per second" besides "hertz" because we habitually only think of hertz as about frequency (cycles per second) and not fractional growth rate. but let's experiment.
The current value of the Hubble parameter is H = 2.20 x 10^-18 hertz = 2.20 attohertz.
The longterm value is H_∞ = 1.83 x 10^-18 hertz = 1.83 attohertz.

We have this Friedmann equation H² - H_∞² = const ρ
where the current energy density of the universe is as I recall something like 0.25 nano joules per cubic meter. Google calculator would call that 0.25 nanopascal. It can't tell the difference between joule per cubic meter and Newton per square meter because they are algebraically the same.

So the constant has to be able to turn a nanopascal of energy density into a square attohertz.

This sounds really bizarre doesn't it? Or does it?

As an experiment I will plug this into the google window:
"8 pi G/(3 c^2) in square attohertz per nanopascal"
I don;t know if it will parse it. I'll paste that in without the quotes, and see.

Wow worked first time! Google came back with:
((8 * pi) * G) / (3 * (c^2)) =
6.2208967 (square attohertz) per nanopascal

 

[marcus]

So now I can tell the energy density of the universe, in metric units, just from knowing the two Hubble rates
the present rate 2.20 attohertz
the longterm rate 1.83 attohertz
I just have to square them and take the difference and divide by 6.22
H² - H_∞² = const ρ
(2.20^2 - 1.83^2)/6.22 this will give ρ in nanopascal---or more exactly in nanojoules per cubic meter
when I put that in google it gives back:
((2.20^2) - (1.83^2)) / 6.22 =
0.2397266881

So the present energy density of the universe (radiation, ordinary matter and dark matter mass energy equiv) is 0.24 nanopascal. Or 0.24 nJ per m³

And in the far distant future when the energy density has thinned out to almost zero, the righthand side will be zero. so the lefthand will be, which means that H will have to almost equal H_∞
which we know it has to because that is what H_∞ (essentially a way of expressing the cosmological constant) is. It is the longterm eventual value of the distance growth rate.

that is to say, an intrinsic, residual spacetime curvature.

 

[bahamagreen]

...everybody just becomes farther apart.
It isn't governed by laws of KE that you are used to and that you invoke. It doesn't take energy to accelerate it. It is dynamic changing geometry, not ordinary motion. It is normal for the growth of distances to be faster than c. The distances to MOST of the galaxies that we can see with a telescope are increasing faster than c. The great majority are.

So the pattern of distance growth (expressed in Hubble Law) should not be thought of as ordinary familiar motion thru space that we are used to. It does not obey the same rules. Just some friendly advice---of course you can think of geometric expansion as motion thru space if you like, but it seems to work out better not to.

I think a source of confusion is thinking about the distance relationship between comoving locations in expansion... the locations are not just becoming further apart, the distance change rate is increasing. The locations are not just comoving, in a sense they are "coaccelerating" which makes one wonder how the locations can remain inertial.

It seems difficult but possible to accept that gravitation is subject to geometry, but much harder to see how acceleration and inertia must also be so... as in, how is it that the distance expansion rate between comoving locations does not subject inertial masses to the usual force of acceleration (why don't the comoving masses resist and slip against the expansion? How does the geometry make the "big picture" of masses accelerating apart not manifest the usual effects of "being pushed apart"?).

Maybe I'm not asking very clearly, but local acceleration is typically regarded as absolute in the sense that motion is not, yet with the comoving expansion distance acceleration, it seems like the "absolute" aspect of acceleration has been demoted and the comoving objects retain their local inertial properties but have lost their inertial relationships to other distant comovers... relationships that would otherwise have been maintained if not due to the expansion geometry.

That still may not be very clearly asked, but some discussion and clarification on how the geometry overrides what would normally be long distance inertial relationships between mutually accelerating objects might be helpful.

 

[wabbit]

@bahamagreen : The comoving objects discussed are indeed inertial, and their proper acceleration is zero - it is only as you say their comoving distance that is changing (and accelerating), but this is not due to proper movement, only to the expansion of space.

why don't the comoving masses resist and slip against the expansion

Think about it this way: each location is the same, a comoving object sees a uniform matter distribution around it : what would it mean for it to "resist the expansion" ? In which direction would it "slip" if it were to do so?

I think the "balloon analogy" (see the excellent explanation linked to in phind's signature) helps in understanding this.

Disclaimer: not a physicist here, just echoing what others have said.

 

[wabbit]

So the present energy density of the universe (radiation, ordinary matter and dark matter mass energy equiv) is 0.24 nanopascal.

That's an interesting way to express it, as a pressure - which we can compare to the standard atmospheric pressure of ~100 kilopascals.
So the average matter/energy/DE pressure of the universe is currently about -2×10^-15 atmospheres :)

I like this, didn't think of it this way.

Also, this is the "(negative) expansion pressure" pushing out against the gravity holding a galaxy together. No wonder galaxies don't expand themselves in response to such a tiny effect. (well, to be fair I should compare it to the "internal" pressure of a galaxy, which may be quite small as well, though much higher than that)

 

[BillyT]

BillyT, you run a risk of confusing your listeners or yourself if you think of the pattern of growing distances as if it were ordinary motion like what we are familiar with. Nobody GETS anywhere by it. ...

Thanks. I understand that the amount of KE depends upon what frame is taken to be at rest; so in Earth's frame, the Earth's translational KE is zero; However, Is it not true that given any choice of a "rest frame," the objects not at rest in it have KE that is increasing with time? (as is their mutual attraction PE). I also know there is no preferred rest point - no "center of the universe" but am in doubt whether or not their is a "mass center" of the universe. - The grand "Barycenter." but doubt it is stationary point in space.

It doesn't take energy to accelerate it. It is dynamic changing geometry, not ordinary motion.

I thought the increase of KE, wrt any point chosen to be "at rest" was due to the work done on the objects with increasing KE (and mutual PE). Is this POV wrong?

 

[wabbit]

I thought the increase of KE, wrt any point chosen to be "at rest" was due to the work done on the objects with increasing KE (and mutual PE). Is this POV wrong?

I think it is simply not applicable in this context. The comoving objects are at rest with respect to each other, they are not moving at all (even though their distance is increasing ! ) and have no kinetic energy associated to this increasing distance.

http://www.phinds.com/balloonanalogy/

Edit "not moving" may or may not be an accepted way to state it, but I think this is a matter of semantics - maybe I should have said "not moving in the way that we usually think of moving". Or just, "no kinetic energy". But this doesn't change the point.

 

[BillyT]

@bahamagreen ... I think the "balloon analogy" ... helps in understanding this. ...

Yes, but:
If gas is flowing into the balloon at constant rate, Its initial Volume, Vo, and initial Diameter, Do will in time T become 8Vo & 2Do by definition of time interval T. During T, the initial surface Area, Ao, increases to 4Ao and the Line between any two dots on the surface, initially Lo long, becomes 2Lo long during T. So we can define an average speed of one point wrt the other as (2Lo - Lo)/ T = Lo/T.

Now with same constant rate of gas inflow, at time 8T the volume is 64Vo, the diameter is 4Do, surface area is 16Ao and the line between those two surface points is 4Lo. So the average speed during the last 7T is (4Lo - 2Lo)/ 7T = (2/7)Lo/T <<< Lo/T

SUMMARY: In the balloon model of the universe, there is strong NEGATIVE acceleration of one galaxy wrt another as their speed wrt to each other is decreasing. I don't think most realize this "defect" of the balloon model.

I'll let someone with more math skill than I have work out how the gas fill rate must accelerate to have points (galaxies) accelerate away form each other.

 

[marcus]

... Is this POV wrong?

I think so. It sounds to me like you are confusing recession (the growth of distance between widely separated objects) with ordinary motion.
It is not appropriate to apply the KE formula to recession speed. Hubble Law distance growth this not like ordinary motion. It is typically faster than c and nobody gets anywhere by it. Everybody just becomes farther apart. No goal or destination is approached. Nobody needs to move thru their surrounding space.

You might try reading in the cosmology FAQ, or the Balloon model sticky. It sounds to me as if you are missing the key concepts of cosmic rest (CMB rest) and universe time (Friedmann model time) that are basic to cosmology.
The Hubble law v = H(t) D cannot be defined without first defining the preferred rest frame, preferred time, proper distance.

 

[BillyT]

stellar

I think it is simply not applicable in this context. The comoving objects are at rest with respect to each other, they are not moving at all (even though their distance is increasing ! ) and have no kinetic energy associated to this increasing distance.

http://www.phinds.com/balloonanalogy/

Edit "not moving" may or may not be an accepted way to state it, but I think this is a matter of semantics - maybe I should have said "not moving in the way that we usually think of moving". Or just, "no kinetic energy". But this doesn't change the point.

Is this POV, sort of by redefining KE, an effort to save "conservation of energy"?

For example, the temperature is the average KE of a large set of particles which interact to maintain a fixed relative speed distribution. That it is their relative speed, is why lead melts at the same temperature in frames moving wrt each other.

Is it meaningful to use the standard definition of temperature to compute the temperature of the universe or one can only give that with the assumption that there is thermal equilibrium between the mater of the universe and the T which fits extremely well to give the distribution of the cosmic background radiation in Planck's equation? If that LTE exists then the universe is very cold < 4K which is hard to swallow with all the stellar fusion occurring..

 

[Quds Akbar]

Einstein once suggested that it might as well be another property of space itself. So I think that as space expands there is more dark energy. Though dark energy may not even exist at all, but most observations suggest it does exist. So it could be just a property of space itself.

 

[wabbit]

Is this POV, sort of by redefining KE, and effort to save "conservation of energy"?

Not at all I think. First conservation energy is not saved in GR, so that would be a failed attempt. But the point is "what is the velocity that goes into KE?". And it is not the recession velocity of comoving objects.

Another related point. - going out on a limb here, the experts will catch me if I'm wrong:
The redshift we see from distant galaxies is not the same as the Doppler effect from a moving source. I picture it like this : as light travels across expanding space, "new space is created" continuously between each peak and trough of the traveling wave, so it gets gradually stretched out as it travels, hence increasing wavelength. The effect comes from what happens during the journey, not from how fast the distant object was moving when it emitted the light.

 

[wabbit]

Einstein once suggested that it might as well be another property of space itself. So I think that as space expands there is more dark energy. Though dark energy may not even exist at all, but most observations suggest it does exist. So it could be just a property of space itself.

I would say this at least sounds like a perfectly reasonable interpretation of the equations - then again, you say Einstein said it first, so I feel quite safe here

 

[marcus]

Yes, but:
If gas is flowing into the balloon at constant rate, ...

You have to want to understand the balloon analogy in the correct way, for it to help you. It takes concentration. Imagine that all existence is concentrated on the infinitely thin balloon surface. There is no inside of the balloon, and no outside space. No gas flowing into the balloon.

the purpose of the analogy is to help understand the geometric relations among the 2d "objects" on the surface. Expansion without a center. All the objects are getting farther apart without anyone of them being central. None of the 2d creatures on the surface can point in a direction which is off the surface. So there is no direction outwards, or inwards.

Like us. You can't point your finger in a direction which is outside the universe. You can't point at the "center" of the expansion. There is no center.
We are the 3d analogs of the 2d creatures on the idealized 2d balloon surface.

The balloon analogy is also useful because it shows how points (galaxies) on the surface can be separating faster than light, and you can picture light wiggling along at a finite speed over the surface going from one point to another.

It is not a PHYSICAL model, it is an illustration to help understand geometric relationships in a changing geometry, by analogy.

 

[wabbit]

I am wondering if we are not trying here to get a little bit too much from analogies - of course they help, and I couldn't do without them. But they are just that: analogies. And any analogy pushed too far is bound to break down.

phinds makes this point far more cogently in his balloon analogy site (referred to in a previous post), which I can only recommend, it really is an excellent read.

Also, what marcus just said.

 

[bahamagreen]

@bahamagreen : The comoving objects discussed are indeed inertial, and their proper acceleration is zero - it is only as you say their comoving distance that is changing (and accelerating), but this is not due to proper movement, only to the expansion of space.

Think about it this way: each location is the same, a comoving object sees a uniform matter distribution around it : what would it mean for it to "resist the expansion" ? In which direction would it "slip" if it were to do so?

I think the "balloon analogy" (see the excellent explanation linked to in phind's signature) helps in understanding this.

Disclaimer: not a physicist here, just echoing what others have said.

Thinking about balloons reminded me of the falling sphere of dust... originally a spherical surface of small particles falls toward an airless planet, the changing gravitational field being fallen through makes the spherical surface elongate in the vertical direction and contract in the lateral directions... these seem to be comoving inertial particles with mutually accelerating distances, but no proper accelerations because they are in free fall.

... thanks/