Dark Energy - is it everywhere?

[Chaos' lil bro Order]

I was thinking about dark energy and whether current understanding puts its distribution as being everywhere in the Universe and evenly so? Like the CMB but homogenous and non fluctuating? I understand that 'dark matter' clumps around certain areas of our own Milky Way so it is quite unlike dark energy. If dark energy is the accelerating force of the Universe to which we owe our current accelerated rate of expansion and its distribution is homogenous and everywhere, can one imagine it exists in your room right now and in your very body, slowly accelerating you outwards, as it were? Far fetched, maybe. I am simply trying to grasp what it means on a personal level as opposed to the more common uses in Cosmology. Is everything simply expanding a tiny bit? You in your chair, your speakers on your desktop, your oaken table and that ruler on your notebook. And if your rule is expanding too, how can one use it to measure the expansion of your speakers?

If anyone knows how dark energy was derived, that would be great too. My guess is it was a necessary number coming out from observation of distant galaxies accelerating outwards faster than predicted given hubble's constant? Thanks.

 

[marcus]

http://arxiv.org/abs/1002.3966/
Why all these prejudices against a constant?
Eugenio Bianchi, Carlo Rovelli
(Submitted on 21 Feb 2010)
The expansion of the observed universe appears to be accelerating. A simple explanation of this phenomenon is provided by the non-vanishing of the cosmological constant in the Einstein equations. Arguments are commonly presented to the effect that this simple explanation is not viable or not sufficient, and therefore we are facing the "great mystery" of the "nature of a dark energy". We argue that these arguments are unconvincing, or ill-founded.
9 pages, 4 figures

 

[phinds]

I was thinking about dark energy and whether current understanding puts its distribution as being everywhere in the Universe and evenly so? Like the CMB but homogenous and non fluctuating? I understand that 'dark matter' clumps around certain areas of our own Milky Way so it is quite unlike dark energy. If dark energy is the accelerating force of the Universe to which we owe our current accelerated rate of expansion and its distribution is homogenous and everywhere, can one imagine it exists in your room right now and in your very body, slowly accelerating you outwards, as it were? Far fetched, maybe. I am simply trying to grasp what it means on a personal level as opposed to the more common uses in Cosmology. Is everything simply expanding a tiny bit? You in your chair, your speakers on your desktop, your oaken table and that ruler on your notebook. And if your rule is expanding too, how can one use it to measure the expansion of your speakers?

If anyone knows how dark energy was derived, that would be great too. My guess is it was a necessary number coming out from observation of distant galaxies accelerating outwards faster than predicted given hubble's constant? Thanks.

The effect that is causing the acceleration of the universe, call it dark energy or whatever, is most likely everywhere as you suggest, but it has zero effect inside objects the size of galactic clusters and smaller (including galaxies, stars, planets, you, me, atoms, etc).

It's like an ant pushing on a house. It isn't that the ant has a little tiny effect, it's that the ant has zero effect because it can't overcome the forces that hold the house on its foundation.

On another point, the current thinking is that your statement about dark matter clustering around galaxies is probably backwards. Dark matter didn't clump around galaxies, galaxies formed around, or along with, clumps of dark matter and in fact galaxies would not have formed at all were there not clumps of dark matter.

 

[mfb]

On another point, the current thinking is that your statement about dark matter clustering around galaxies is probably backwards. Dark matter didn't clump around galaxies, galaxies formed around, or along with, clumps of dark matter and in fact galaxies would not have formed at all were there not clumps of dark matter.

To extend this: The common way to model the evolution of the early universe is to model the gravity of dark matter only - regular matter just follows and clumps in the region of high density.

 

[Naty1]

It appears so far that dark energy density is uniform in vacuum space. It's negative pressure acts as gravitational repulsion tending to expand space. The net effect is that more and more space results with a constant energy density leading to increasing expansion pressure; as matter flows with the expansion and becomes more widly separated the effects of a matter dominated universe give way to the current inflationary epoch.

As noted by others, such a weak force has no apparent effect on people and planets and solar systems for example. But there is no model either for such interactions, that is, the uniformity and homogeneaty conditions of the cosmological model which leads to the cosmological constant do not apply in such non-uniform [lumpy] environments.

There is a discussion of an interesting new paper on EMERGENT GRAVITY here:

https://www.physicsforums.com/showthread.php?p=3984153#post3984153

 

[Chaos' lil bro Order]

The effect that is causing the acceleration of the universe, call it dark energy or whatever, is most likely everywhere as you suggest, but it has zero effect inside objects the size of galactic clusters and smaller (including galaxies, stars, planets, you, me, atoms, etc).

r.

Is this like the same idea where galaxies move away from one another according to hubble's law? I have read the correct metaphor for the Universe's expansion and in particular how galaxies move along on this expansion with respect to one another (again hubble's law) is best thought of as the 'dots on a balloon' metaphor. You blow up the balloon and the dots move away from one another, just like some galaxies on the expanding fabric of space.
I mean, why would this dark energy 'effect' only be felt on galactic clusters and on nothing smaller? I am curious about this point. Is its energy so very low that on local scales, even our Earth's atmosphere and magnetic fields would dissipate it? It needs and extremely large mass like a globular cluster to impart its force? I have trouble with physics that does not involve particles and forces. Just exactly what models of dark energy to we have?
I shall read that referenced paper as well, thank you Marcus.

 

[jcsd]

It;s actually a really good question, on a large scale it must be everywhere, though on smaller scale it's still an open question if dark energy is evenly distributed.

 

[marcus]

It;s actually a really good question, on a large scale it must be everywhere, though on smaller scale it's still an open question if dark energy is evenly distributed.

That's strange. I never heard that. Can you link to any evidence of spatially varying value of the cosmological constant? Any review paper that mentions possible spatial unevenness?
You've got me curious.

 

[andrewkirk]

The effect that is causing the acceleration of the universe, call it dark energy or whatever, is most likely everywhere as you suggest, but it has zero effect inside objects the size of galactic clusters and smaller (including galaxies, stars, planets, you, me, atoms, etc).

It's like an ant pushing on a house. It isn't that the ant has a little tiny effect, it's that the ant has zero effect because it can't overcome the forces that hold the house on its foundation.

In that example the ant has no effect because the house is locked to its foundations by electrostatic forces. But within a galactic cluster the stars are freely falling and hence responsive to the slightest variation in the curvature of spacetime. Surely the curvature of spacetime within a galactic cluster will be slightly different with a small positive lambda from what it would be with a zero lambda, wouldn't it? If so, wouldn't that make the effect negligible (ie an unmeasurably small change in the shape of the timelike geodesic a star follows) rather than zero?

 

[andrewkirk]

That's strange. I never heard that. Can you link to any evidence of spatially varying value of the cosmological constant? Any review paper that mentions possible spatial unevenness?
You've got me curious.

Could it be something to do with moduli? The wikipedia article on dark energy seems to imply that moduli is/are one postulated form of dark energy that varies over space:

"Two proposed forms for dark energy are the cosmological constant, a constant energy density filling space homogeneously,[3] and scalar fields such as quintessence or moduli, dynamic quantities whose energy density can vary in time and space. "

 

[Chaos' lil bro Order]

I am not a 100% on whether the WMAP information of the CMB or Hubble's Law observations have shown dark matter in any specific part of the Universe, but rather they show it as a mathematical necessity to explain the acceleration of the Universe's expansion give our current Standard Model. Do we have any evidence specifically of it?

 

[phinds]

I am not a 100% on whether the WMAP information of the CMB or Hubble's Law observations have shown dark matter in any specific part of the Universe, but rather they show it as a mathematical necessity to explain the acceleration of the Universe's expansion give our current Standard Model. Do we have any evidence specifically of it?

I assume you mean dark energy, not dark matter, since your statement is about dark energy even thought you say dark matter

"Dark energy" is a name we give to something not at all understood at any fundamental level, but there is a lot of diverse experimental evidence that SOMETHING is causing the accelerated expansion of the universe so we call it dark energy.

 

[Mark M]

I am not a 100% on whether the WMAP information of the CMB or Hubble's Law observations have shown dark matter in any specific part of the Universe, but rather they show it as a mathematical necessity to explain the acceleration of the Universe's expansion give our current Standard Model. Do we have any evidence specifically of it?

Firstly, dark matter has nothing to do with the acceleration of the universe. Dark energy does. Despite the names, they are totally different things, and we have direct evidence of dark matter.

We have evidence that the universe is accelerating, so that qualifies as evidence for dark energy. The question isn't whether it exists or not, but what form it takes. Most people would probably say it's a cosmological constant, a built in negative curvature into Einstein's Field Equation that would function as dark energy.

 

[marcus]

... Most people would probably say it's a cosmological constant, a built in negative curvature into Einstein's Field Equation ...

Right. In other words not an "energy" at all---as far as we know. I'm told Roger Penrose has been pointing this out, but I haven't got a source link for that yet. Maybe someone knows one and will supply it.

So far it's just a curvature constant that appears naturally in the EFE, and would not require an energy field or "vacuum energy" of any sort to cause it. It COULD be due to an energy field, or the constant in the equation might have some other explanation, or it might simply be one of a small number of fundamental constants of nature, like Planck's constant h, or Newton's G, that we don't feel a need to explain (at least for the time being.)

"Vacuum curvature" would be a better expression to use. "Dark energy" is one of these misleading terms like "Big Bang" that gets rooted in people's imagination and distorts their understanding. Maybe it reminds them of sex, or something delightful like that. Or maybe it's just a tiny bit scary and causes a little shiver in the mind. Anyway terms like Big Bang and Dark Energy are going to be hard to root out of the language.

I'll go with calling Lambda the vacuum curvature. (Whether we call it a positive or negative curvature just depends on how you write the EFE, what sign you put in front of Lambda when you write the equation.)

Here's a link to a favorite article about the cosmo constant, I'm sure you've seen it but maybe someone else reading here hasn't.
Why all these prejudices against a constant?
http://arxiv.org/abs/1002.3966/

 

[ryan albery]

I've been trying to track it down, but on the world's slowest internet connection and unable to open .pdf files... does anyone know what the actual rate of acceleration of our expanding universe? How quickly, with an actual number, is the expansion of the universe accelerating (volume^3/seconds^2)?

 

[marcus]

I've been trying to track it down, but on the world's slowest internet connection and unable to open .pdf files... does anyone know what the actual rate of acceleration of our expanding universe? How quickly, with an actual number, is the expansion of the universe accelerating (volume^3/seconds^2)?

The universe has no definite speed of expansion. How much a distance increases depends on the size of the distance. Remember these are largescale distances far larger than the scale of a solar system or a galaxy.

Put in percentage growth terms, the current estimated rate of expansion is 1/139 of one percent per million years.

This percent rate has been decreasing and according to standard cosmology is expected to continue decreasing, approaching a lower limit of 1/163 of a percent. But if you fix on the distance to a particular galaxy and could track that distance for a long time you would see its growth speed up. Somewhat like compound interest or exponential growth. The slope gets steeper with time because the distance you're taking percentage of gets longer (even though the percentage rate may be declining slightly.)

In order to get an acceleration quantity (which you asked for) we'd have to pick a distance and imagine a galaxy at that distance and study how fast the distance to it was growing in actual speed terms, and how the growth was accelerating. I'll see if I can come up with some numbers. Or someone else may beat me to it.

Remember that Hubble law expansion is not like ordinary motion because nobody gets anywhere by it. Everybody just gets farther apart. That's why the Hubble law is about distances between objects or observers which are at rest with respect to the ancient light i.e. relative to the microwave background.

 

[phinds]

I've been trying to track it down, but on the world's slowest internet connection and unable to open .pdf files... does anyone know what the actual rate of acceleration of our expanding universe? How quickly, with an actual number, is the expansion of the universe accelerating (volume^3/seconds^2)?

Anecdotally, the best way to remember it is this: Even though the universe is expanding, it is still going to be hard to find a parking place. Why? Well, if you could magically draw a pair of parking place lines in intergalactic space, it would take about 20 BILLION years for them to move far enough apart to accommodate another car. (this fits w/ the figure Marcus gave).

So pretty clearly, on small scales it might as well not be happening.

On the other hand, galaxies at the edge of our observable universe are receeding from us at about 3c, which shows that on large scales the effect is pretty staggering.

 

[marcus]

Ryan you asked for some idea of acceleration and to get an actual speed that distance is increasing I have to pick a distance to examine. A very common one is 13.9 billion lightyears.

Most of the galaxies which we can see with a telescope are farther away than that, but it's a handy distance scale that astronomers use a lot. Let's define a scale a(t) that increases with time and equals that distance now a(now) = 13.9 billion LY.

That distance is increasing at a speed that you can work out. what is 1/139 percent of 13.9 billion LY? Well it is 1/139 percent of 13900 million LY which is exactly 1 million LY. That is how much it increases per million years. So it is increasing at the rate c.

Most of the galaxies we can see as of today are farther than that so the distances to them are increasing faster than that (they aren't getting anywhere just farther apart, it's geometry change not usual motion so no rule is violated.)

So what about acceleration? Well that particular distance is growing with speed a'(now) = c , so what about its growth acceleration a"(now)? I'm using the calculus notation prime and doubleprime for first and second derivatives.

The acceleration is a certain percentage of the speed of light, per million years.
a"(now) = 1/236 of a percent of c, per million years.

So if you take a galaxy (assume it is at rest relative to the background) that is at a distance of 13.9 billion LY. then the distance to that galaxy is growing at rate c
and after a million years it will be growing at a slightly faster rate
namely (1 + 1/23600) c.

You can change all this to "kilometer per second" terms if you want. Just replace c
by 300,000 km/s
The amount the distance growth speed increases is 300000/23600 = 12.7 km/s

So if the distance starts out increasing at rate 300,000 km/s then after a million years it will be increasing at a speed of around 300,012 km/s or so.

I think that's right, I'll check it or if I made an error maybe someone will catch it for me.

This acceleration people talk about is really not so much percentage wise and seems almost negligible unless you think in terms of very long intervals of time.

 

[Chronos]

Confusion arises when you try to translate recession velocities into the local inertial frame of distant galaxies, some of which are receeding at nearly 3c. Obviously, they are not receeding from their neighbors at anywhere near such a speed.

 

[DeepSpace9]

How come we cannot figure out what Dark Matter is made out of, if it is indeed real?

If it is everywhere, why isn't it as simple as, taking a jar glass, leave it outside for a hour, put the top on and observe the Matter?

 

[Naty1]

How come we cannot figure out what Dark Matter is made out of

Dark matter cannot be seen, not directly observed, in so far as is known; apparently it neither emits nor absorbs light or other electromagnetic radiation. So identifying it as separate and distinct from other stuff in the jar would be difficult. And any gravitational effect from the dark matter in a jar is below any threshold we can hope to measure.

 

[Chaos' lil bro Order]

This is a great discussion guys. Many thanks. Especially phinds and Marcus, for his brilliantly and simply written calculation. That was nice of you to take the time.

If I am understanding correctly, the Dark energy/ lambda vacuum curvature/Cosmological Constant are one and the same. I like that lambda vacuum curvature (LVC) the best as well. Given prior posts, it seems the most clinically accurate and devoid of sensationalism, that is most useful when actually trying to understand an effect correctly. Let me then build a simple metaphor for the Universe at large and have you all pick at and improve it.

I start with the idea of comparing space to a big sheet of rubber membrane. Massive objects or energy densities on this membrane will deform it. A sun will 'sit' on this membrane and 'push' it down, thus creating a 'dimple' where the sun is now 'sitting'. This dimple may draw other objects towards it if they are near enough to fall into its well. They may also fall into its orbit. This dimple is effectively thought of as gravity then. Gravity is mass or energy, deforming space and causing 'dimple wells'.

Now then. This rubber membrane of space is being stretched in every direction and our suns, our galaxies, our clusters are all 'sitting' on this membrane and going for the ride, as it stretches outwards in every direction at the same rate, with no 'preferred' direction of stretching. Note that in this model, the rubber membrane is two dimensional. Picture then, a large flat piece of rubber in the shape of a circle 10ft in diameter and a cm thick. On it are marbles of varying sizes and masses that simulate galaxies and clusters. This membrane is curved downwards along its edges so that it convex. The marbles start rolling outwards towards the edges of the membrane and appear to be moving very fast before they roll off the edge, with respect to marbles more near the center of the circular membrane. Their co-moving distance with respect to one another, near the membrane's edges, is also much much greater than the same co-moving distance between marbles near the center.
This model fails in several ways, I know, but its decent in that it shows gravity correctly as a curvature of space caused by massive densities, as opposed to some attractive force that 'pulls' objects in towards it. Objects are not pulled into black holes, they fall into the 'dimple well' in the membrane of space, where the black hole is 'sitting'. I quite like this 'dimple well' term, its an easy visual imo.

Now then, Marcus' LVC' would be an extra curvature on this rubber membrane that would turn it even more convex. We can guess the mass of all the marbles on the membrane and their rough distribution 'sitting' on top of it, and we can infer that the membrane is more convex than Einstein wanted to believe. The marbles are moving outwards faster than his theories had predicted. The LVC is the culprit then. We need this extra curvature to explain how these marbles are flying off the membrane so fast. What's even odder is that this membrane, which in its convex shape, appear somewhat like an open umbrella, is changing curvature more and more every day. Its becoming more convex. The umbrella is closing faster and faster and the marbles are falling off of it at greater speeds.

 

[ryan albery]

Thanks for the responses, but now I'm even more confused. I was under the impression that the accelerated expansion (acceleration of volume) of the universe was a constant, perhaps represented by the cosmological constant, and it's independent of distance?

 

[phinds]

Thanks for the responses, but now I'm even more confused. I was under the impression that the accelerated expansion (acceleration of volume) of the universe was a constant, perhaps represented by the cosmological constant, and it's independent of distance?

Yes, that's correct. Why do you now think that someone has said it isn't ?

Did you not understand my comments about how it has a tiny effect on small distances and a big one on big distance. It is, as Marcus pointed out, a percentage of the distance.

Do you think that if you expand a 1-foot ruler by 10% you will get the same absoulte amount of extra length that you would if you expanded a million-mile ruler by 10% ?

 

[ryan albery]

I think (hopefully) that I understand that expansion is a function of distance, but my question was regarding the acceleration of that expansion. I get that this expansion is a function of distance, but regardless of distance, the acceleration of this expansion (dark energy) is measured to be constant, everywhere?

 

[mfb]

If everything extends by 10% per year now and by 11% per year in 100 years, this is independent of the distance. However, if you want to write this as "meters per year^2", you will get different values for small and large objects, similar to the ruler example.

 

[marcus]

I've been trying to track it down, but on the world's slowest internet connection and unable to open .pdf files... does anyone know what the actual rate of acceleration of our expanding universe? How quickly, with an actual number, is the expansion of the universe accelerating (volume^3/seconds^2)?

Ryan you asked for some idea of acceleration and to get an actual speed that distance is increasing I have to pick a distance to examine. A very common one is 13.9 billion lightyears.

Most of the galaxies which we can see with a telescope are farther away than that, but it's a handy distance scale that astronomers use a lot. Let's define a scale a(t) that increases with time and equals that distance now a(now) = 13.9 billion LY.

That distance is increasing at a speed that you can work out. what is 1/139 percent of 13.9 billion LY? Well it is 1/139 percent of 13900 million LY which is exactly 1 million LY. That is how much it increases per million years. So it is increasing at the rate c.

Most of the galaxies we can see as of today are farther than that so the distances to them are increasing faster than that (they aren't getting anywhere just farther apart, it's geometry change not usual motion so no rule is violated.)

So what about acceleration? Well that particular distance is growing with speed a'(now) = c , so what about its growth acceleration a"(now)? I'm using the calculus notation prime and doubleprime for first and second derivatives.

The acceleration is a certain percentage of the speed of light, per million years.
a"(now) = 1/236 of a percent of c, per million years.

So if you take a galaxy (assume it is at rest relative to the background) that is at a distance of 13.9 billion LY. then the distance to that galaxy is growing at rate c
and after a million years it will be growing at a slightly faster rate
namely (1 + 1/23600) c.

You can change all this to "kilometer per second" terms if you want. Just replace c
by 300,000 km/s
The amount the distance growth speed increases is 300000/23600 = 12.7 km/s

So if the distance starts out increasing at rate 300,000 km/s then after a million years it will be increasing at a speed of around 300,012 km/s or so.

This acceleration people talk about is really not so much percentage wise and seems almost negligible unless you think in terms of very long intervals of time.

Thanks for the responses, but now I'm even more confused. I was under the impression that the accelerated expansion (acceleration of volume) of the universe was a constant, perhaps represented by the cosmological constant, and it's independent of distance?

I think (hopefully) that I understand that expansion is a function of distance, but my question was regarding the acceleration of that expansion. I get that this expansion is a function of distance, but regardless of distance, the acceleration of this expansion (dark energy) is measured to be constant, everywhere?

Hi Ryan, I appreciate your keeping on asking, shows you really want to understand. I'll try to help. First you have to realize that nobody is saying that there is some definite acceleration that is the same for all distances. There isn't.
And nobody is saying there is a definite km/s growth that is the same for all distances. There isn't.
A lot of the talk in popular media is a bit sensational. "Dark energy" is a bit hypey too. We don't know that there actually an energy causing the growth of distances.

If you look at a fixed length distance, the amount that distance will grow next year is actually LESS than the amount the same length distance will grow this year.
That is clear from the model and if sloppy journalism gives you a different impression then it is just sloppy hype journalism. And the decline is expected to continue. It is a very gradual decline in the absolute growth and it is consistent with what has been observed and called "acceleration".

Basically folks are talking about is extremely slow exponential growth of distances like growth of a savings accounts at a very small (declining) rate of interest. You realize that a savings account "accelerates" because the principal gets bigger so the dollar growth rate is proportionately bigger. And it can even "accelerate" while the bank is slowly lowering the rate of interest. Do you picture that OK?

 

[ryan albery]

Thanks Marcus, I'm definitely (confusedly) trying to understand. I understand your bank account example, I think, so far as reference frames go. If I do grasp this correctly, then the cosmological constant is like the fine structure constant, in that it's a dimensionless constant, by the nature of how we define the acceleration?

 

[marcus]

Thanks Marcus, I'm definitely (confusedly) trying to understand. I understand your bank account example, I think, so far as reference frames go. If I do grasp this correctly, then the cosmological constant is like the fine structure constant, in that it's a dimensionless constant, by the nature of how we define the acceleration?

I'll tell you what I've found seems to be the best way to approach it.
As Einstein originally introduced Λ, it was a reciprocal area. It was not dimensionless. One over area or one over length squared is a unit of curvature and spacetime curvature is unfamiliar. It's easier to grasp if you multiply by c squared.
Λc² is the square of a fractional growth rate. The square of a number-per-unit-time. Can you work that out?

The most concrete immediately understandable physical meaning of the constant Λ is
that Λc²/3 is the square of the longterm eventual fractional growth rate of distance.

In the standard cosmic model, the ΛCDM model the current growth rate of distance is 1/139 of a percent per million years
and this rate is slowly declining and the model says it will level out after some tens of billions of years at a lower rate of 1/163 of a percent per million years.

The square of that eventual very slow rate is, in fact, equal to Λc²/3 .

This is the practical significance of the measured value of Λ.

The actual expansion of distances then will be slower than it is now. If you take a particular distance and watch it for a million years, these days it will increase by 1/139 of one percent. And far far in future if you watch the same distance it will increase by only 1/163 of one percent.
But of course like your savings account at the bank, the growth of any distance will be ACCELERATING because as the principal grows the absolute dollar increment which is a fixed percentage grows. And the same thing happens with any distance if you keep patiently watching.

So hypesters keep yammering "acceleration acceleration ACCELERATION DARK ENERGY!"
But it is simply familiar very slow stuff like a savings account with extremely low (and slowly declining) rate of interest. Like 1/139 of one percent per million years is not such an exciting rate of interest and even that is gradually diminishing.

BTW one of the things that IS interesting is that if you look at what the Hubble expansion Law actually says it is not talking about galaxies whizzing around it is talking about distances between stationary observers---observers at rest with respect to the background provided by the ancient CMB light.
So the Hubble Law does not affect distances inside bound structures like galaxies or clusters of galaxies. It comes into play over much larger distances. So I should have been saying largescale distances when I was talking earlier, but it gets tedious always saying largescale. I think you probably realize that I was talking about intergalactic or intercluster scale distances. And they should be distances between observers at rest wrt ancient light, measured at a particular moment of universe time. That's part of the fine print of Hubble Law.