Dark Energy - is it everywhere?


by Chaos' lil bro Order
Tags: dark, energy
Chronos
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Jul28-12, 02:17 AM
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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
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#20
Jul29-12, 04:13 PM
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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
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Jul29-12, 04:26 PM
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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
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Aug4-12, 03:43 PM
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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
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Aug9-12, 01:11 PM
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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
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Aug9-12, 01:25 PM
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Quote Quote by ryan albery View Post
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
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Aug9-12, 01:53 PM
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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
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Aug9-12, 02:54 PM
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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
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Aug9-12, 04:42 PM
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Quote Quote by ryan albery View Post
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)?
Quote Quote by marcus View Post
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. Lets 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.
Quote Quote by ryan albery View Post
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?
Quote Quote by ryan albery View Post
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
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Aug9-12, 04:57 PM
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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
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Aug9-12, 05:00 PM
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Quote Quote by ryan albery View Post
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.


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