Could Vacuum Energy Be the Key to Understanding Dark Energy?

[TrickyDicky]

This is what I mean by repulsive -- the presence of vacuum energy lessens the acceleration due to gravity felt by two test masses.

If that were the case I could actually see the conection suggested in previous posts between "Dark energy" and "Dark matter" since if the presence of vacuum energy really lessens the acceleration due to gravity felt by two test masses, that over huge space volumes would have the effect of a modified gravity and could explain unexpected galactic rotational curves and cluster dynamics that the "dark matter" hypothesis tries to fix. As this is obviously not the case I doubt very much your premise about repulsive gravitation.

 

[bapowell]

If that were the case I could actually see the conection suggested in previous posts between "Dark energy" and "Dark matter" since if the presence of vacuum energy really lessens the acceleration due to gravity felt by two test masses, that over huge space volumes would have the effect of a modified gravity and could explain unexpected galactic rotational curves and cluster dynamics that the "dark matter" hypothesis tries to fix. As this is obviously not the case I doubt very much your premise about repulsive gravitation.

This is not my premise. This is the standard lore. Pick up any cosmology textbook and read about inflation, late-time accelerated expansion, gravitational effects of vacuum energy, etc. The reason that dark energy fails to explain galactic rotation curves is because galaxies are gravitationally bound objects. Expansion, whether it be accelerated or otherwise, does not operate on such scales.

I wish the idea that vacuum energy lead to accelerated expansion was my idea -- I might be waiting in the wings for a Nobel Prize. Alas, this was the brilliant discovery of Guth, Linde, and others in the 80's. I'm surprised that you are apparently unaware of this.

 

[TrickyDicky]

The reason that dark energy fails to explain galactic rotation curves is because galaxies are gravitationally bound objects.

Sure but if the gravitational effects of "dark energy" were to have influence in the outer part of the galactic disk, at that region it wouldn't be "bound" in the Newtonian sense (see below).
You would be introducing an element not accounted for in Newtonian gravity, Newtonian law of gravitation certainly knows nothing about any "dark energies" or vacuum energies producing "repulsive" gravitational forces.

Expansion, whether it be accelerated or otherwise, does not operate on such scales.

Accelerated expansion (not just expansion as expansion itself is not related to "dark energy") if(big if) it really was vacuum energy with "repulsive" gravitational effect would certainly have to operate from the scales at which its gravitational magnitude allowed it and that would depend on the figures attributed to its energy-density, using the upper limit of the cosmological constant, the vacuum energy in a cubic centimeter of free space has been estimated to be 10−15 Joules (source: Wikipedia), if we take that value seriously it certainly would be noticeable in the galactic outer areas and cluster scales due to its cumulative effect, don't you think?

I wish the idea that vacuum energy lead to accelerated expansion was my idea -- I might be waiting in the wings for a Nobel Prize. Alas, this was the brilliant discovery of Guth, Linde, and others in the 80's. I'm surprised that you are apparently unaware of this.

In fact IIRC it was first suggested by McCrea in the late 60's that Lambda could be interpreted as vacuum-energy, I'm perfectly aware of these hypothesis, but I'm free to consider them provisional conjectures; when I said "your premise" I was taking a rhetorical license meaning "the one promise you are currently using", certainly, didn't mean it was your idea

The notion that it is the standard lore in every cosmological book is debatable to some extent but I haven't read All Cosmology books edited so I won't argue with you about this point.

 

[bapowell]

Sure but if the gravitational effects of "dark energy" were to have influence in the outer part of the galactic disk, at that region it wouldn't be "bound" in the Newtonian sense (see below).
You would be introducing an element not accounted for in Newtonian gravity, Newtonian law of gravitation certainly knows nothing about any "dark energies" or vacuum energies producing "repulsive" gravitational forces.

Nobody's talking Newtonian physics here. My statement regarding the expansion due to dark energy not affecting bound structures is relativistic. This is the conclusion that GR reaches on this topic.

Accelerated expansion (not just expansion as expansion itself is not related to "dark energy") if(big if) it really was vacuum energy with "repulsive" gravitational effect would certainly have to operate from the scales at which its gravitational magnitude allowed it and that would depend on the figures attributed to its energy-density, using the upper limit of the cosmological constant, the vacuum energy in a cubic centimeter of free space has been estimated to be 10−15 Joules (source: Wikipedia), if we take that value seriously it certainly would be noticeable in the galactic outer areas and cluster scales due to its cumulative effect, don't you think?

No, this is patently false. Cosmological expansion is not operative on galactic or planetary scales because these are gravitationally bound structures (nor does it operate on the scale of atoms, which are electromagnetically bound, etc.) Another way to look at it is the following: how does one get an expanding universe out of Einstein's Equations? One conjectures a homogeneous and isotropic geometry (the Friedmann-Robertson-Walker spacetime) with a homogeneous and isotropic matter/energy density (this works for anisotropic models as well, but for simplicity we'll stick to isotropic.) The resulting expansion/contraction is uniform. Meanwhile, a galaxy is far from homogeneous and isotropic, and Einstein's Equations will not give you an expanding spacetime for such a matter distribution -- the universe expands on scales only on which it is sufficiently smooth.

If your suggestion were true, then we'd be able to observe galaxies, solar systems, etc growing in size along with the expansion. We simply don't see this.

In fact IIRC it was first suggested by McCrea in the late 60's that Lambda could be interpreted as vacuum-energy, I'm perfectly aware of these hypothesis, but I'm free to consider them provisional conjectures; when I said "your premise" I was taking a rhetorical license meaning "the one promise you are currently using", certainly, didn't mean it was your idea

Sure, you are free to consider them conjectures and you needn't accept that inflation happened or that the universe is currently accelerating. That's not what this discussion is about. The whole basis of our discussion stemmed from the fact that you seemed to be suggesting that vacuum energy did not lead to accelerated expansion. You are not free to have your own opinions on this matter -- it derives directly from GR. Unless, of course, you have problems with GR. Then that's a different story.

 

[TrickyDicky]

Hmm... I think you are defending at the same time one thesis and its contrary and that's not fair, and you are arguing against a strawman as I'm not the one that supports the idea of vacuum energy having repulsive gravitational effects, I'm just deriving logical consequences of that IMO confusing hypothesis.

Nobody's talking Newtonian physics here. My statement regarding the expansion due to dark energy not affecting bound structures is relativistic. This is the conclusion that GR reaches on this topic.

GR reaches no conclusion about "dark energy", how could it? It was susrprisingly discovered in 1998, almost 75 years after GR formulation, you can try to fit DE in the equations but currently I believe there is no consensus in the scientific community as to how exactly do that.
Besides I mentioned Newtonian gravitation in the context of "dark matter", do you mean it's not used in the galactic rotation curves calculations?

No, this is patently false.

Sure, that's my position, as I said I'm deriving consequences of a wrong approach.
BTW, I don't have any problems with GR, in fact is my favourite theory. I tend to be very cautious with unwarranted consequences attributed to GR specially when they are not coherent with the general picture.

 

[bapowell]

I'm not claiming to know what dark energy is. I'm simply saying that, if you put a stress energy into Einstein's Equations with \rho \propto -p, you get all the effects that I'm talking about -- including accelerated expansion and no effect on galaxy rotation curves. I'm not sure what two theses you think I'm simultaneously defending, nor am I aware of the strawman that you think I'm using. I'm saying that you can't argue that vacuum energy doesn't have gravitationally repulsive effects. This follows from two facts: that vacuum energy has \rho \propto -p and that GR is correct. It isn't a matter of opinion.

 

[TrickyDicky]

I'm simply saying that, if you put a stress energy into Einstein's Equations with \rho \propto -p, you get all the effects that I'm talking about -- including accelerated expansion and no effect on galaxy rotation curves. This follows from two facts: that vacuum energy has \rho \propto -p and that GR is correct.

I agree with those two facts and yet your conclusions are not the only ones possible from them, you are allowing yourself certain degree of interpretation from those facts so you must admit that there might be other interpretations of the same facts. We can agree to disagree, I'll leave it here.

 

[nismaratwork]

I agree with those two facts and yet your conclusions are not the only ones possible from them, you are allowing yourself certain degree of interpretation from those facts so you must admit that there might be other interpretations of the same facts. We can agree to disagree, I'll leave it here.

Um... I won't. I've been reading this, and I don't see this other possible interpretation THAT WORKS. You claim it exists, would you please show me, or link or otherwise support that claim?

 

[TrickyDicky]

Um... I won't. I've been reading this, and I don't see this other possible interpretation THAT WORKS. You claim it exists, would you please show me, or link or otherwise support that claim?

Well, bapowell made it clear that his interpretation is the one followed by most people in the community, I'm not completely sure about that but just in case that is the opinion of PF mentors too, I can't support it here any more than I've done, I don't want to risk an infraction, (still got many questions to ask), sorry.

 

[nismaratwork]

Well, bapowell made it clear that his interpretation is the one followed by most people in the community, I'm not completely sure about that but just in case that is the opinion of PF mentors too, I can't support it here any more than I've done, I don't want to risk an infraction, (still got many questions to ask), sorry.

Ahhhh... I see. Well, thanks for being up-front about that, I'm not trying to get you into any kind of trouble.

 

[Delta2]

No idea what this has to do with Automatic Teller Machines. I am not proposing a modified gravity -- just GR. In the weak field limit in the presence of a CC, \Lambda, one has for the Newtonian potential \Phi:

\nabla^2 \Phi = -\nabla g = 4\pi G \rho - \Lambda

where g is the gravitational acceleration. This becomes

g = -\frac{GM}{r^2} + \frac{\Lambda r}{3}

and you can see the \Lambda is a repulsive contribution.

Dont know much about GR and cosmological constant but can't CC be negative?

 

[bapowell]

Dont know much about GR and cosmological constant but can't CC be negative?

Yes. That geometry, called anti de Sitter space, is of particular interest to string theorists.

 

[Imax]

Dark energy is assumed to exist because of observations made on distant galaxies. The more distant a galaxy, the greater the red shift. So, for example, a galaxy at 10 billion light years has a greater red shift that a galaxy at 1 billion light years. This is interpreted to mean that the farther a galaxy is from our point of observation, the earth, the greater its’ speed, leading to the conclusion that the expansion of the Universe is accelerating.

What if instead of interpreting the observed red shift as a function of distance, it was interpreted as a function of time? So, for example, 10 billion years ago (i.e. a galaxy at 10 billion light years) a galaxy would have a greater red shift than a galaxy 1 billion years ago (i.e. a galaxy at 1 billion light years). That would mean that 1 billion years ago, the speed of a galaxy was less than that of a galaxy 10 billion years ago. This could be interpreted to mean that the expansion of the Universe is decelerating with time.

 

[nismaratwork]

Dark energy is assumed to exist because of observations made on distant galaxies. The more distant a galaxy, the greater the red shift. So, for example, a galaxy at 10 billion light years has a greater red shift that a galaxy at 1 billion light years. This is interpreted to mean that the farther a galaxy is from our point of observation, the earth, the greater its’ speed, leading to the conclusion that the expansion of the Universe is accelerating.

What if instead of interpreting the observed red shift as a function of distance, it was interpreted as a function of time? So, for example, 10 billion years ago (i.e. a galaxy at 10 billion light years) a galaxy would have a greater red shift than a galaxy 1 billion years ago (i.e. a galaxy at 1 billion light years). That would mean that 1 billion years ago, the speed of a galaxy was less than that of a galaxy 10 billion years ago. This could be interpreted to mean that the expansion of the Universe is decelerating with time.

AFAIK: Because this would be inconsistent with observations, and experiment since Hubble first chewed on a pipe.

 

[bapowell]

What if instead of interpreting the observed red shift as a function of distance, it was interpreted as a function of time? So, for example, 10 billion years ago (i.e. a galaxy at 10 billion light years) a galaxy would have a greater red shift than a galaxy 1 billion years ago (i.e. a galaxy at 1 billion light years). That would mean that 1 billion years ago, the speed of a galaxy was less than that of a galaxy 10 billion years ago. This could be interpreted to mean that the expansion of the Universe is decelerating with time.

10 billion years ago, a galaxy 10 billion light-years away would have had a redshift of around 0. The key is that today that galaxy has a greater redshift than a galaxy 1 billion light-years away. The galaxy at 10 billion light-years has a greater recession velocity today than the galaxy 1 billion light-years away simply because it is further away from us. This is a general trend that follows from Hubble's Law, and doesn't by itself tell us anything about the expansion history of the universe. What matters here is the detailed dependence of redshift on distance -- this is provided by observations of type 1a supernovae.

 

[Imax]

AFAIK: Because this would be inconsistent with observations, and experiment since Hubble first chewed on a pipe.

Not necessarily. The observation is the same (i.e. red shift), but the interpretation is different.

 

[nismaratwork]

Not necessarily. The observation is the same (i.e. red shift), but the interpretation is different.

That still conflicts with observations (see bapowell's post!).

 

[71STARS]

Gravity has nothing to do with so-called dark energy, in my opinion. Gravity is the attraction between two core entities. Its function in Empty Space diminishes greatly. When dark matter is found to be a steam/mist/quantum foam, the energy associated with it may be minimal as to be nil. However, the quantity of dark matter (aka pressure ether in Dwyer's), the sheer volume of dark matter, this would be the factor of force, but one that is completely non-hindering. Einstein's CC was strangely on point, even though it was not created for such.

 

[nismaratwork]

Gravity has nothing to do with so-called dark energy, in my opinion. Gravity is the attraction between two core entities. Its function in Empty Space diminishes greatly. When dark matter is found to be a steam/mist/quantum foam, the energy associated with it may be minimal as to be nil. However, the quantity of dark matter (aka pressure ether in Dwyer's), the sheer volume of dark matter, this would be the factor of force, but one that is completely non-hindering. Einstein's CC was strangely on point, even though it was not created for such.

What the HELL are you talking about? Gravity is, currently, believed to be the geometry of spacetime; you're describing Newton's view of gravity. Then you start rambling...

 

[TrickyDicky]

Not necessarily. The observation is the same (i.e. red shift), but the interpretation is different.

Simplyfying a lot. What is known as accelerated expansion is just an observation made from 1997 and well confirmed since, that a type of Supernovae, the type Ia, that due to its features is considered a good "standard candle" for large distances doesn't look as bright from here as the models predicted. This is done by comparing observations in the two main sources of information in astrophysics:spectrometry (redshift) and photometry (brightness).
Redshift can be used as an independent measure of the distant an object such a galaxy is, and if we have a good standard candle, that is, a reliable way to guess the intrinsic brightness of a distant object we can relate that supposed intrinsic brightnes with the brightnes we measure with our photometers.
And what was observed was that certain Supernovae redshifts when converted to distance didn't fit with the expected brightness, it appeared less bright than models usually predicted, and that could logically be interpreted as the Supernovae being farther away for a given redshift than the distance the model predicted for that redshift.
Considering redshift as velocity it leads to think that the Supernovae is accelerating from us, thus accelerated expansion. As simple as that, although the implications for cosmology are not as simple.

 

[PhilKravitz]

We should be a little careful here. Dark energy isn't repulsive anymore than ordinary matter is attractive. Rather, a homogeneous distribution of dark energy will cause spacetime to accelerate -- this is a gravitational phenomenon. So it's more correct to say that dark energy is gravitationally repulsive, and ordinary matter is gravitationally attractive.

So as the universe gets bigger there is more dark energy and the rate of expansion increases. What does this feedback lead to? Does it create a BANG!? If so, what happens next? If not, how fast will the universe be expanding in the future? Is there a limit to the expansion rate?

 

[nismaratwork]

So as the universe gets bigger there is more dark energy and the rate of expansion increases. What does this feedback lead to? Does it create a BANG!? If so, what happens next? If not, how fast will the universe be expanding in the future? Is there a limit to the expansion rate?

Less than 'c' in their own frame...

 

[PhilKravitz]

Less than 'c' in their own frame...

If I understand correctly during inflation points in the universe had the space between them increase faster than the speed of light. Can this happen at some point in the future due to dark energy repulsive force?

 

[bapowell]

So as the universe gets bigger there is more dark energy and the rate of expansion increases. What does this feedback lead to? Does it create a BANG!? If so, what happens next? If not, how fast will the universe be expanding in the future? Is there a limit to the expansion rate?

Good question Phil. The destiny of the universe depends on the nature of the dark energy. In its simplest incarnation, dark energy can be chosen to have a constant energy density (a cosmological constant.) In this case, as the universe expands, the dark energy in a comoving volume increases. The (logarithmic) rate of expansion given by the Hubble parameter,

H = \frac{\dot{a}(t)}{a(t)}.

where a(t) is the scale factor (governing in the growth of length scales in the universe. ) In this case, when the dark energy is constant, the Hubble parameter is constant as well. The universe goes right on expanding.

However, consider the case in which the dark energy density grows, \dot{\rho} > 0. Then, it can be shown that a future singularity is hit (see: http://prl.aps.org/abstract/PRL/v91/i7/e071301) because the scale factor goes to infinity in finite time. This has been termed the Big Rip, and occurs at a time determined by

t_{\rm rip} - t_0 \propto |1+w|^{-1}H_0^{-1}

where the subscript '0' denotes present values, and w=p/\rho, with w<-1 for \dot{\rho} > 0. Dark energy that behaves in this way is called phantom energy, and has met with serious theoretical difficulties. In any case, as an effective equation of state, it leads to a cataclysmic dooms day.

 

[nismaratwork]

If I understand correctly during inflation points in the universe had the space between them increase faster than the speed of light. Can this happen at some point in the future due to dark energy repulsive force?

bapowell gave the good answer... I was just going to say, "nobody knows... we just know some options."

It is a very good question indeed.

 

[bapowell]

If I understand correctly during inflation points in the universe had the space between them increase faster than the speed of light. Can this happen at some point in the future due to dark energy repulsive force?

This is a popular misconception. Even during ordinary, decelerated expansion, there exist points in the universe that separate at speeds surpassing that of light. This follows simply from Hubble's law: v=Hr, where v is the relative velocity of the two points and r their separation. When their separation reaches a value of r=c/H then you can see that the relative velocity surpasses that of light. Nothing funny going on -- this is what defines an important distance known as the Hubble radius.

The main distinction to be made with inflation is that during decelerated expansion, the Hubble distance grows faster than the expanding spacetime, gradually illuminating (literally) distant regions of the universe. During inflation, the background spacetime is expanding more rapidly than the Hubble distance is increasing with the result that the boundary of the observable universe becomes an event horizon. During inflation, the expansion can (and did) pull things outside of the observable universe.

 

[nismaratwork]

This is a popular misconception. Even during ordinary, decelerated expansion, there exist points in the universe that separate at speeds surpassing that of light. This follows simply from Hubble's law: v=Hr, where v is the relative velocity of the two points and r their separation. When their separation reaches a value of r=c/H then you can see that the relative velocity surpasses that of light. Nothing funny going on -- this is what defines an important distance known as the Hubble radius.

The main distinction to be made with inflation is that during decelerated expansion, the Hubble distance grows faster than the expanding spacetime, gradually illuminating (literally) distant regions of the universe. During inflation, the background spacetime is expanding more rapidly than the Hubble distance is increasing with the result that the boundary of the observable universe becomes an event horizon. During inflation, the expansion can (and did) pull things outside of the observable universe.

That was... elegantly put!

 

[Imax]

Redshift can be used as an independent measure of the distant an object such a galaxy is, and if we have a good standard candle, that is, a reliable way to guess the intrinsic brightness of a distant object we can relate that supposed intrinsic brightnes with the brightnes we measure with our photometers.
And what was observed was that certain Supernovae redshifts when converted to distance didn't fit with the expected brightness, it appeared less bright than models usually predicted, and that could logically be interpreted as the Supernovae being farther away for a given redshift than the distance the model predicted for that redshift.

OK, maybe I’m a fuzz brain (i.e full of dark matter), but I don’t understand why differences in photometric (i.e. brightness) and spectroscopic (i.e. red shift) measurements of type 1a supernovae imply an acceleration in the expansion of the Universe.

 

[PhilKravitz]

During inflation, the background spacetime is expanding more rapidly than the Hubble distance is increasing with the result that the boundary of the observable universe becomes an event horizon. During inflation, the expansion can (and did) pull things outside of the observable universe.

This is a new idea to me. Very interesting. Thanks bapowell.

 

[PhilKravitz]

However, consider the case in which the dark energy density grows, \dot{\rho} > 0. Then, it can be shown that a future singularity is hit (see: http://prl.aps.org/abstract/PRL/v91/i7/e071301) because the scale factor goes to infinity in finite time. This has been termed the Big Rip, and occurs at a time determined by

t_{\rm rip} - t_0 \propto |1+w|^{-1}H_0^{-1}

where the subscript '0' denotes present values, and w=p/\rho, with w<-1 for \dot{\rho} > 0. Dark energy that behaves in this way is called phantom energy, and has met with serious theoretical difficulties. In any case, as an effective equation of state, it leads to a cataclysmic dooms day.

bapowell thanks for the reference I will go and read it. And I quite enjoy the terminology "Big Rip" and "phantom energy".