# More on dark energy

1. Oct 1, 2009

### S.Vasojevic

I am starting this thread because this is something Sylas and me were discussing off topic on another thread, but I would welcome more clarification on this.

If I understand this correctly galaxies are not moving apart because there is a force acting on them which overcomes gravity, and accelerate their mass, but simply because more space is being "stuffed" in between them?

If above is correct wouldn't that imply that between receding galaxies there is constant gain in gravitational potential energy which comes not from expense of some other form of energy, but from expanding space. Wouldn't that be a violation of first law of thermodynamics?

2. Oct 1, 2009

### friend

You know, I'm really not sure how you would measure the difference between expanding space itself or expanding through a non-expanding space. Can anyone enlighten me? Thanks.

3. Oct 1, 2009

### Wallace

No, you are mixing motion with acceleration. The reason galaxies move apart at any given moment is because they were doing some a moment ago, just like any other motion than obeys Newton's first law (or equivalently the relativistic generalisation of it).

Now, the reason the rate of recession is accelerating is because of the action of a force, stronger than that of gravity when the current density of the universe is considered (technically again we can describe this more sensibly by the relativistic generalisation of 'force' but that's a technicality). We suppose that force is applied by dark energy, but that isn't known for sure and is not well understood yet.

As for the space part, this is just the result of all of this, not the cause. In other words, because galaxies are all moving apart the distance between them increases, which you can describe as the expansion of space if you wish. You shouldn't consider that this is cause of the recession of galaxies though, that's getting it backwards. The details of how much extra space appears (again if you choose to use that description) depends entirely on the physics of dark energy (and other cosmological parameters).

The take home message is that the increasing distance is the result of the physics, not a physical principle in and of itself.

4. Oct 1, 2009

### Ich

There is no difference on small scales, just as cosmological redshift is nothing but a combination of gravitational and doppler redshift. "motion through space" and "expansion of space" are two descriptions for the same thing.
However, on larger scales, and if spacetime curvature becomes relevant, things become weird. For example, you could add many positive velocities to get zero at the end of the day. In such a case, the expanding space description is easier to grasp. The balloon model turns out to be quite appropriate then - as long as you don't glue your galaxies to the balloon.

5. Oct 1, 2009

### Ich

No.
If there is gravitational potential energy (i.e. mass), then the gain comes from kinetic energy. The expansion (or "motion") slows down. In the early nineties, people generally thought that this is what happes, but they had disturbing hints that this could not be all.
In 1998, they had enough data to - tentatively, then - deduce that the expansion accelerates instead.
Weird as it may sound, this assumption solved some serious problems (those "hints" were pointing at it), and newer data confirmed it.
So now, as we stil don't know exactly what's going on, we postulate that the universe behaves as if the vacuum had negative pressure, like something repulsive filling everything. That's where the accelerating galaxies get their energy from.
The energy comes from the negative pressure: if something with negative pressure expands, it does negative work - i.e. it gains energy. Thats how this "dark energy" keeps itself alive.

6. Oct 1, 2009

### S.Vasojevic

No, I am not. Just bad choice of words.

And again, how is that not a violation of principle of conservation of energy? Something repulsive is filling everything, accelerating galaxies, and constantly adding energy to them.

7. Oct 1, 2009

### apeiron

I think what is really at stake here is the question: is there more space about now than there was just a moment ago? And change normally seems to demand some action.

Putting aside dark energy complications, you can then say this change is inertial. But then what is it that is freely moving here? It is not the galaxies if you take the more usual raisins in a rising cake view of their "motion". So how does the idea of inertial motion apply to the vacuum exactly? A general expansion seems still the right word.

8. Oct 2, 2009

### Chalnoth

In that respect it's not any different than an attractive force, where kinetic energy is added as two objects get closer and closer together (diverging to infinity as the separation becomes zero for point-like particles).

In either case the energy equation is balanced once you take into account potential energy as well as kinetic energy.

9. Oct 2, 2009

### Amanheis

Don't worry about global energy conservation, we have to discard it since there is no timelike killing vector in the Robertson-Walker spacetime. Energy is only conserved locally.

10. Oct 2, 2009

### S.Vasojevic

Thanks Amanheis.
I know most of you guys has chewed this stuff over and over again, but for someone new to modern cosmology, there is a great deal of controversy. Things like:
Cosmological redshift - doppler or expanding space?
Dark energy - galaxies are not moving anywhere, space is expanding or is it that force acting on them is accelerating them?
BB- universe did not expanded to empty space, space was created as Universe expanded. Since it is expanding ever since we can assume that space is being created as of today.
Then comes inevitable question - how can you tell the difference between expanding space, and stuff accelerating apart?
Physics is not so about mechanisms, as it is about accurate predictions, and maybe much of this things may be described as chicken - egg problem. But if we do not build mental constructs, and try to understand what is "really" going on, we are not longer exploring.

When we speak about gravity, we are slowly abandoning concept of force field in favor of concept that matter curves space, and consequently matter will act as curved space dictates. What about dark energy? Is force that it puts on objects result of change in geometry of space?

11. Oct 2, 2009

### Amanheis

Well first of all, space would expand even without dark energy, just not accelerated. But galaxies would still appear to move away from us.
And before we go on I'd like to remark that it is a non-trivial thing to compare velocities of non-local objects. This has to do with the so-called parallel transport of tangent vectors on curved manifolds. I don't want to go into the details right here, you can read up on it if you feel prepared for some elementary differential geometry.
Now to the difference between expanding space and accelerated objects. Surprisingly there is a unique frame of reference in the universe, and that is the frame of reference in which the cosmic microwave background radiation appears isotropically. This is the frame of reference "in which the big bang happened", so to say. Objects that are in rest relatively to that frame of reference are said to be comoving. If you'd start to accelerate out of this frame, you would see a doppler blueshift of the CMB in the direction of your acceleration, and a redshift behind you. The earth (and the whole milky way) is actually moving with a velocity of 400km/s relative to the CMB frame of reference.
Very distant galaxies, that is galaxies that are not gravitationally coupled, can now experience an increase of distance while still being comoving the entire time due to expansion of space.

12. Oct 2, 2009

### Chalnoth

Cosmological redshift is definitively not the Doppler effect. You can go and do the calculations yourself, but suffice it to say that the redshift we observe doesn't match with the recession velocity of the objects we're observing.

As Amanheis noted, this is a feature of any expanding universe, not of just one with dark energy. But the answer is that this is a bad question. The matter moving apart and the expansion of space are one and the same thing. One way to look at it is this. Here are Einstein's equations:

$$G_{\mu\nu} = T_{\mu\nu}$$

On the left hand side we have the Einstein tensor. This tensor describes the curvature of space-time. It describes things like, for example, the expansion of space.

On the right hand side we have the stress-energy tensor. This tensor describes the matter/energy/pressure of the matter. When we talk about how matter behaves, we're talking about the right hand side of this equation. So when we say, for instance, that the galaxies are moving further part, we're talking about the right hand side of the equation.

The fact that the two sides of the equation are identically equal, however, means that these are just two different ways of describing the exact same thing. Whether we discuss it in terms of the galaxies or space is irrelevant.

Dark energy isn't a different force. It's still gravity that's acting here. The dark energy (whatever it is) basically is just a form of matter that has an interesting ratio of pressure to energy density such that gravity acts on this form of matter to cause expansion.

13. Oct 2, 2009

### apeiron

So Amanheis, are you agreeing that space actually does expand - that there are more countable locations over time, to put it crudely.

And I think what most people find bothersome about this is the implication that information is not being conserved, there is more of something being created freely - in open system Hoylean fashion.

But then as you say, temperature of the CBR is also a way to establish a reference frame. And here, with time, we would expect to see a local cooling.

So to me, this dual aspect view of what is happening helps restore conservation (and I think this mirrors Chalnoth's point, though he was talking about mass and gravitational potential). More space is matched obviously by more cooling. So the local and global views are in accord. Just measured in different ways.

The natural yardstick then for what is "really happening" would be the red-shifting of photons. Follow these and you can see expansion and cooling at the same time, with total energy conserved.

Or this is how Charlie Lineweaver put it....
The entropy density s of a radiation field of temperature T is s ~ T3. The entropy S in a given comoving volume V is S = s V. Since the comoving volume V increases as the universe expands, we have V ~ R3. And since the temperature of the microwave background goes down as the universe expands: T ~ 1/R, we have the result that the entropy of a given comoving volume of space S ~ R-3 * R3 = constant. Thus the expansion of the universe by itself is not responsible for any entropy increase. There is no heat exchange between different parts of the universe. The expansion is adiabatic and isentropic: dSexpansion = 0.

14. Oct 3, 2009

### Chronos

Asperion, you are stuck on the idea of an absolute reference frame. Get over it, it doesnt work in fhe face of irreftuable observational evidence.

15. Oct 3, 2009

### apeiron

I don't believe that is what I'm saying at all. Or at least I'm not looking for the standard static reference frame but instead the standard dynamic equilibrium point. So this is the expanding/cooling world anchored by the triad of constants, or balance points, h, g and c.

So yes to the dynamic "absolutes" that can create an emergent frame of reference, but no to a reference frame that exists statically as a Newtonian stage.

16. Oct 3, 2009

### Chalnoth

Newtonian mechanics also had no absolute reference frame.

17. Oct 3, 2009

### apeiron

Someone better let Wiki know fast......

===============

Classical mechanics, which includes relativity, assumes the equivalence of all inertial reference frames. Newtonian mechanics makes the additional assumptions of absolute space and absolute time.

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

These notions imply that absolute space and time do not depend upon physical events, but are a backdrop or stage setting within which physical phenomena occur. Thus, every object has an absolute state of motion relative to absolute space, so that an object must be either in a state of absolute rest, or moving at some absolute speed.[2] To support his views, Newton's provided some empirical examples: according to Newton, a solitary rotating sphere can be inferred to rotate about its axis relative to absolute space by observing the bulging of its equator, and a solitary pair of spheres tied by a rope can be inferred to be in absolute rotation about their center of gravity (barycenter) by observing the tension in the rope.

In today's classical mechanics, the notion of absolute space is replaced by the idea of inertial frames of reference.

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

18. Oct 3, 2009

### Chalnoth

Well, he may have thought this, but it's nowhere to be found in his equations.

19. Oct 3, 2009

### apeiron

OK, so now that we've established that I'm not a believer in absolute reference frames and Newton probably was, it would be great to return to the OP's query - which I have never seen answered in a completely satisfactory way.

I offered what to me seems the route to a commonsense understanding of where the "more space" is coming from, based on a reputable source. Am I off the mark for some reason?

20. Oct 4, 2009

### keepitmoving

isn`t it a fact that space expands in the absence of gravity. Does that expanding space come from the extra dimensions decompactifying into our 3 dimensions?