Why is Dark Energy required ?

[dougettinger]

In the initial Big Bang a certain amount of energy was supplied to the known universe. Matter was created from this energy. Energy was left over to expand this matter until the forces of gravity due to this matter supposely slow down or stop the expansion. From Newton's First Law could it not be theorized that enough energy is left over to keep expanding the universe with the given matter ? Why is Dark Energy required ?

I am hoping to find a simple answer for the invention of Dark Energy.

Doug Ettinger
Pittsburgh, Pa

[bystander]

(Wikimedia Commons/Azcolvin429)

Wikipedia: Lambda-CDM model

Visible matter and energy is that which we can directly observe (the stuff of planets, stars, and galaxies). According to observations, there was not enough matter to explain gravitational effects (galaxy rotation anomalies, gravitational lensing, galaxy clustering). Cold dark matter was proposed to account for this. With all this matter, the universe should collapse under its own weight, but the universe is expanding, and at an accelerating rate. To account for these observations, dark energy was proposed (the lamda in ΛCDM). That is as simple as I can make it.

[dougettinger]

So what happens when the accelerating rate reaches the velocity of light ?

Doug Ettinger
Pittsburgh, PA

[rstevenson]

Think of a car travelling at a steady rate on a rubber highway which is being stretched at an ever increasing rate. No matter how fast the stretching occurs, the car keeps going at its own rate. (We better make that a unicycle to avoid issues of expansion rate differential between the front and rear axles.)

Similarly, the local velocity of local chunks in space -- say, our galaxy or even our solar system -- would not change. All that would happen is that more and more of the universe would "wink out" like a lightbulb being turned off, as more of the universe went beyond the sphere which is visible to us. In extremis, this would leave us in a cold, dark and lonely place, if there was any "us" to notice.

Rob

[dougettinger]

I understand you point. But my point is that according to theory nothing can go faster than the speed of light. So if the edge of the universe or the unicycle achieves the speed of light and keeps accelerating - what happens to this matter ? It appears to me that this entire universe is inside a black hole where nothing can escape. Perhaps all matter is converted back to energy ? I am certainly no cosmologist - just curious.

Doug Ettinger
Pittsburgh, PA

[Chris Peterson]

I understand you point. But my point is that according to theory nothing can go faster than the speed of light.

That's not true. Most of the Universe is moving faster than the speed of light with respect to the rest of the Universe. What can't go faster than the speed of light is information. As long as the regions are causally disconnected, there is no violation of physical law. The fact that universal expansion is actually not linear with distance doesn't change anything. But it does mean there needs to be an energy source. Otherwise, gravity would be slowing down the expansion rate.

[hstarbuck]

Think of a car travelling at a steady rate on a rubber highway which is being stretched at an ever increasing rate. No matter how fast the stretching occurs, the car keeps going at its own rate. (We better make that a unicycle to avoid issues of expansion rate differential between the front and rear axles.)

Similarly, the local velocity of local chunks in space -- say, our galaxy or even our solar system -- would not change. All that would happen is that more and more of the universe would "wink out" like a lightbulb being turned off, as more of the universe went beyond the sphere which is visible to us. In extremis, this would leave us in a cold, dark and lonely place, if there was any "us" to notice.

Rob

How about 100 unicycles spread out evenly on a circular rubber track--they can be moving or not. If as the track stretches (representing the expansion of space itself in between galactic clusters) linear distance between each unicycle on the track doubles every second, then average velocity can be measured from one bike wrt any other using linear distance divided by time. The further away a bike is to the observer the faster it will be going (*****before this analogy blows up I need to set limits that say you only observe 49 bikes away max). So any bike observing the 49th bike away will find it traveling away with greater velocity and acceleration than those closer. However, another observer on a bike will find that it observes a different velocity for each of the other bikes than the first observer. Recall that the bikes may or may not be moving--and certainly nowhere near the speed of light. If allowed to continue, and scaled up universally, the furthest bikes from an observer bike will show redshifts corresponding to velocities greater than c with respect them, but nearest observers to same bike (v>c) will observe lower velocities relative to themselves (probably v<c).

It is not the doppler effect(shift in wavelength and frequency due to motion of source) that allows for redshift greater than c because the galaxies are not moving through space faster than c. It is the space in between expanding that shifts the light corresponding to velocities greater than c. Mindbending to say the least and I hope I have this correct. Evidently it is the dark energy that fills the space as it is expanding.

[dougettinger]

I am not sure how one differentiates between space stretching and the velocity of the emitter using redshift.

Doug Ettinger
Pittsburgh, PA

[Chris Peterson]

I am not sure how one differentiates between space stretching and the velocity of the emitter using redshift.

They are very different in terms of underlying theory. There is no conclusive way to separate them in observational data, however, since they both produce the same result. They can often be separated using statistical methods: if you observe a galaxy cluster, you expect the same cosmological redshift, so the variation in redshift values is reasonably attributed to a conventional Doppler component caused by the orbital motion of the galaxies around one another (or some other peculiar motion). And in some cases, simply knowing what you are looking at helps: over cosmological distances, Doppler redshift will be tiny compared with cosmological redshift; when looking at things much closer, cosmological redshift will be small or zero, so it can be assumed that observed redshift is Doppler.

[dougettinger]

Let me try to simplify this explanation. If Doppler shift is used to measure a faraway galaxy's rotation and the expected rotation is different, then the difference could be the redshift of the cosmological distance. Is this true ?

I just discovered that galaxies can be traveling faster than the speed of light. Wow.

Doug Ettinger
Pittsburgh, PA

[Chris Peterson]

Let me try to simplify this explanation. If Doppler shift is used to measure a faraway galaxy's rotation and the expected rotation is different, then the difference could be the redshift of the cosmological distance. Is this true ?

What do you mean by "the expected rotation is different"? All you can measure in the distant galaxy is redshift. If you measure one redshift at one limb, and a different redshift at the other limb, you can conclude that this is Doppler shift, and the difference gives you the rotation rate along the viewing axis. You can also look at the absolute shift of known emission lines, and determine the peculiar velocity. This will be a Doppler measurement for nearby galaxies, and a cosmological redshift measurement for distant galaxies.

I just discovered that galaxies can be traveling faster than the speed of light.

I wouldn't say that. It would be more accurate to say that nothing prevents parts of the Universe from separating from other parts at greater than c. But those parts are then causally disconnected. You can't really say any thing is moving faster than light.

[jman]

So if area 1 is moving at 0.5c and area 2 is moving the same speed in the opposite direction, they are separating at c. - seems easy enough.
Is there a limit, could you say the fastest that two areas could separate is 2c?

[Chris Peterson]

So if area 1 is moving at 0.5c and area 2 is moving the same speed in the opposite direction, they are separating at c. - seems easy enough.
Is there a limit, could you say the fastest that two areas could separate is 2c?

There are no limits. Two regions can be moving faster than c relative to each other by any multiple. The limitation is that once their relative velocity reaches c, they are no longer causally connected- no information can flow from one to the other. They are outside each others observable universe.

[Henning Makholm]

So if area 1 is moving at 0.5c and area 2 is moving the same speed in the opposite direction, they are separating at c. - seems easy enough.
Is there a limit, could you say the fastest that two areas could separate is 2c?

Chris's answer is correct, but I'd like to emphasize the most primitive fact you need to know: The lightspeed limit only applies to bodies (particles, whatever) that are close to each other. It is purely a Special Relativity rule, and is not generally true in General Relativity, except that GR approximates SR within sufficiently small regions of spacetime. Cosmological distance is far beyond the validity of SR.

[Henning Makholm]

The limitation is that once their relative velocity reaches c, they are no longer causally connected- no information can flow from one to the other. They are outside each others observable universe.

I am not sure this is true in general. How do you define "relative velocity" here?

If we measure distances between galaxies along hypersurfaces in spacetime defined by a common age since the big bang (isn't this the customary choice?), and relative velocity as the derivate of this with respect to either galaxy's time, then in a homogeneous universe Hubble's law holds exactly at arbitrary distances, and as long as it expands there will be galaxies with arbitrarily large relative velocities.

On the other hand, in some (but not all) big-bang models, such as Milne's one or (less obviously) the classical "open" universe with no cosmological constant, any event is eventually visible everywhere else. In such a universe your limitation would be false. It may or may not be true in our universe, but if it is, it will have to be for reasons subtle enough not to apply in Milne's model.

[Chris Peterson]

The limitation is that once their relative velocity reaches c, they are no longer causally connected- no information can flow from one to the other. They are outside each others observable universe.

I am not sure this is true in general. How do you define "relative velocity" here?

Of course, like any non-mathematical discussion involving GR, meanings are often a bit vague.

I simply mean that two objects with a relative velocity greater than c do not affect each other. That doesn't mean that a pair of causally disconnected events will always remain so. Or am I misunderstanding you here?

In any case, I think the level of the answer was adequate for the level of the question, which did not really seem to invite a discussion of alternate metrics or fairly obscure descriptions of the Universe.

[jman]

Um - ya. It's gotten well over my head. But thanks, I really appreciate the effort.

[Henning Makholm]

Sorry for hijacking the thread, jman. Feel free to ignore this tangent and continue your own questions.

I simply mean that two objects with a relative velocity greater than c do not affect each other. That doesn't mean that a pair of causally disconnected events will always remain so. Or am I misunderstanding you here?

If I understand you correctly, you're saying that two galaxies whose relative velocity is >c now will not be able to communicate unless and until they slow down to <c somewhen in the future?

That is not true. Consider Milne's universe. Here the relative velocity between two given galaxies is constant. If it is >c now, it will stay >c forever. But we can still communicate with them. A photon they emit now will initially seem to recede from us, but as the Hubble coefficient decreases (inversely with the universe's age), the photon will eventually be allowed to approach us instead.

[Chris Peterson]

That is not true. Consider Milne's universe.

Like I said, I think the answer given was suitable for the question asked <g>. There's already one brain stretching discussion involving a fairly academic application of GR. I'd just as soon avoid letting this particular thread drift too far into esoteric territory. The question was, is there some limit on how fast two objects (or regions of space) can recede from one another, and I think "no" is a fair answer.

[Henning Makholm]

The question was, is there some limit on how fast two objects (or regions of space) can recede from one another, and I think "no" is a fair answer.

"No" is indeed a correct answer to that question.
However, your answer was not "no".
Your answer was "no, and if they recede at c it means they are no longer causally connected".

Q: What is 2+2?
A: It's 4, and 3+5 is 16.
B: How do you get 16 for 3+5?
A: We already have a thread on advanced addition. The question was 2+2, and I think "4" is a fair answer.

[swainy]

Chris Peterson wrote:I simply mean that two objects with a relative velocity greater than c do not affect each other. That doesn't mean that a pair of causally disconnected events will always remain so. Or am I misunderstanding you here?


If I understand you correctly, you're saying that two galaxies whose relative velocity is >c now will not be able to communicate unless and until they slow down to <c somewhen in the future?

That is not true. Consider Milne's universe. Here the relative velocity between two given galaxies is constant. If it is >c now, it will stay >c forever. But we can still communicate with them. A photon they emit now will initially seem to recede from us, but as the Hubble coefficient decreases (inversely with the universe's age), the photon will eventually be allowed to approach us instead.

http://en.wikipedia.org/wiki/Milne_model

How can I consider Milne's universe, When it says things like : There is no expansion of space?

tc

[Chris Peterson]

How can I consider Milne's universe, When it says things like : There is no expansion of space?

For that reason and others, I'd say this particular model has been invalidated and does not describe the physical universe.

[Henning Makholm]

That is not true. Consider Milne's universe. Here the relative velocity between two given galaxies is constant. If it is >c now, it will stay >c forever. But we can still communicate with them. A photon they emit now will initially seem to recede from us, but as the Hubble coefficient decreases (inversely with the universe's age), the photon will eventually be allowed to approach us instead.

How can I consider Milne's universe, When it says things like : There is no expansion of space?

How does the fact that Wikipedia makes a strange fuzzy statement (or even the fact that the model does not describe our universe) prevent you from considering how velocities and causality would work in an universe described by the model?

Milne's model is a particularly simple instance of a class of models known as Robertson-Walker metrics. When Chris made his claim, I assumed that he was envisioning an argument for it that would work in all Robertson-Walker metrics. Such an argument would necessarily be flawed, as I have shown by exhibiting some instance of a Robertson-Walker metric in which the conclusion is false.

The possibilities that logically remain are (1) the claim is not actually true about our universe either, (2) my proposed counterexample is not a counterexample, due to faults in my reasoning, or (3) it is true in our universe, but for reasons that do not apply to all Robertson-Walker models.

I had hoped to learn something interesting, either (2) where my reasoning fails, or (3) finding our what particular properties of our universe leads to the causal limitation Chris asserts. Unfortunately, Chris seems unwilling to share the reasons he had for making the claim in the first place, so it looks like I'll have to resign to learning nothing at all.

[The Code]

Milne's model is a particularly simple instance of a class of models known as Robertson-Walker metrics. When Chris made his claim, I assumed that he was envisioning an argument for it that would work in all Robertson-Walker metrics. Such an argument would necessarily be flawed, as I have shown by exhibiting some instance of a Robertson-Walker metric in which the conclusion is false.

Oh you mean this?

http://en.wikipedia.org/wiki/Friedmann% ... ker_metric

Can You show me where its flawed? Please, And Why.

tc

[Henning Makholm]

Milne's model is a particularly simple instance of a class of models known as Robertson-Walker metrics. When Chris made his claim, I assumed that he was envisioning an argument for it that would work in all Robertson-Walker metrics. Such an argument would necessarily be flawed, as I have shown by exhibiting some instance of a Robertson-Walker metric in which the conclusion is false.

Oh you mean this?
http://en.wikipedia.org/wiki/Friedmann% ... ker_metric
Can You show me where its flawed? Please, And Why.

There is nothing wrong about Robertson-Walker metrics.

There is (unless I'm mistaken, and then I'd appreciate having pointed out where) something wrong with the the proposition that
IF (a) the universe is described by a Robertson-Walker metric,
THEN (b) two galaxies that recede from each other at speed >c are causally decoupled until their mutual speed drops below c.