Increase of dark energy with expansion of universe

[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/

 

[BillyT]

... 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.

I'm 99.99% sure you are correct here; but part of the photons growing longer is that they: (1) may have originated in "deeper gravitation well" than the one the "fell into to be detected." & (2) Gravity is a force with infinite range (to speak of it as force created by mass) so the strength of the well they are "climbing out of" is not falling off just by inverse r^2 due to their speed of light travel away from their source, but the source is moving away from where they are at any instant too, making their separation from go as inverse R^2 where R is probably ever so slightly greater than the distance they have traveled (if gravity field is instantous at least.)

 

[wabbit]

I'm 99.99% sure you are correct here; but part of the photons growing longer is that they: (1) may have originated in "deeper gravitation well" than the one the "fell into to be detected."

Yes, this must play a role, as well as any proper motion of the source - but these are in addition to the expansion effect - and even if the photon comes from excited hydrogen emission of a small interstellar gas cloud at the confines of the galaxy (no deep well), I believe the redshift is pretty much the same, at least for distant galaxies where the expansion effect should dominate pretty much everything else - after all a recession velocity close to c is a big effect, we see gamma rays in the infrared I think for some very distant sources (hmm better check that one I pulled it out of a hat - edit : seems OK http://arxiv.org/abs/astro-ph/0502218).

 

[BillyT]

... But the point is "what is the velocity that goes into KE?". And it is not the recession velocity of comoving objects. ...

One does not need any point to be fixed, if LTE conditions apply, to define a temperature. It is the relative speeds, not absolute speed that define the total KE of an interacting system of stars (or the melting point of lead) - Those temperaturs do not depend upon the choice of frame. Lead melts at the same temperature in all frames.

If we assume that gravitational interactions have established LTE for the mater of the universe, then the KE in the definition of the universe's temperature is "frame invariant."

 

[wabbit]

You make me doubt, but if what you say is right then your KE involves supraluminal velocities, which sounds weird, does SR even allow that?

And are sure sure there is such a thing as the total KE of the universe? We know it isn't true for energy as a whole, but perhaps KE is OK, I don't know...

Edit:-not contesting your point for an interacting system, galaxy or such of course, but its applicability to global expansion.

Edit: I'm pretty sure I've stretched by limited understanding far enough here already if not too far, so I'll watch from the sidelines now and let more qualified posters bring us forward.

 

[BillyT]

You make me doubt, but if what you say is right then your KE involves supraluminal velocities, which sounds weird, does SR even allow that?

Yes SR even allows that. What you (or a particle) can not do is start at the origin of a coordinate system and then move away from that origin at greater than C.

Except perhaps in the first femto, femto seconds after the big bang, during the "expansion" - I don't know is C was a speed limit then.

 

[wabbit]

Yes SR even allows that. What you (or a particle) can not do is start at the origin of a coordinate system and then move away from that origin at greater than C.

I meant, applying the energy formula to compute KE with a supraluminal speed. Even with the GR formula this doesn't seem possible - OK this being clarified about what my question was, I will truly retreat and watch for a while.

 

[Phynos]

I'm 99.99% sure you are correct here; but part of the photons growing longer is that they: (1) may have originated in "deeper gravitation well" than the one the "fell into to be detected."

You seem to only be considering the time light spends escaping gravitational wells. Since the universe is highly homogeneous on large scales, we would expect that on average the energy lost by a photon due to it's motion out of a gravitational well will be countered by the energy gained by that same photon due to it's motion into a gravitational well. Gravitational red shift for the beginning of it's journey and blue shift for the end. So I don't think this can account for cosmological red shift.

 

[Nugatory]

The underlying problem here is that kinetic energy is, in general, only defined locally.

In a flat spacetime, we can choose the simultaneity convention that is under our noses (choose any inertial frame, use it to assign a $t$ coordinate to every event everywhere, declare all events with the same $t$ coordinate to be simultaneous) and we'll find that in that particular case we can extend our local frame everywhere and find that energy is globally conserved. In a curved spacetime, that trick doesn't work because there is no global inertial frame; we cannot use the coordinate velocities of objects to define a useful globally conserved quantity.