Why Doesn't Dark Energy Expand Galaxies?

[g.lemaitre]

I'm pretty sure this answer is not known but it always good to double check. Dark energy causes space to expand but the space inside a galaxy does not. Does anyone know why? I'm pretty sure the answer is not known, so I have a guess as to why this might be the case. Particles send out gravitational waves that cause the space around them to attract other particles. When these particles are not present the space is free of this attraction and will therefore expand. In brief, where there are massive objects space contracts or at least does not expand, where there are no massive objects space expands. Not much of an explanation but it's just a conjecture anyway.

 

[Shovel]

I'm pretty sure this answer is not known but it always good to double check. Dark energy causes space to expand but the space inside a galaxy does not.

I imagine it is similar to the reason why a slinky, when held vertically from one end over the grand canyon, will not stretch to reach the canyon floor. Instead it will stretch to the point where the force of gravity equals the spring force of the slinky, and remain in that state indefinitely. Someone please correct me if I am mistaken.

 

[Ibix]

I'm not certain that your cosmology is 100% textbook, but the answer to why space does not expand inside galaxies is simple: it does. It's just that gravity is strong enough that the expansion of space does not drag matter along with it. Shovel's comparison is apt; another one would be to place coins, representing galaxies, on a rubber sheet, representing space. Stretch the sheet - why do the coins not stretch too? Because the internal forces holding the coins together are stronger than the frictional forces trying to tear them apart.

Remember that the expansion of space is very slight. Every second you get an extra kilometre of space spread over about fifty megaparsecs - and our galaxy is only about thirty kiloparsecs across. That means that the expansion of the space under the galaxy is around half a metre per second. In that same second, the Earth has moved around twenty kilometres round the Sun, the speed it has to move not to spiral in. Gravity is much stronger.

 

[g.lemaitre]

why space does not expand inside galaxies is simple: it does. It's just that gravity is strong enough that the expansion of space does not drag matter along with it. Shovel's comparison is apt; another one would be to place coins, representing galaxies, on a rubber sheet, representing space. Stretch the sheet - why do the coins not stretch too? Because the internal forces holding the coins together are stronger than the frictional forces trying to tear them apart.
.

Excellent explanation. I'm really glad I dispelled that illusion. Thanks.

 

[phinds]

try this:

www.phinds.com/balloonanalogy

 

[Drakkith]

Well, remember that we cannot observe space itself expanding. Even the concept of "space itself" expanding is nearly nonsensical. Instead, we can only observe the behavior of matter and light within space. If a galaxy isn't expanding I don't think we can say that space IS expanding or ISN'T expanding inside it, only that the expansion process does not cause objects which are bound to recede from each other.

 

[DaveC426913]

I always go back to the "pennies on a balloon" analogy.

Take a half-filled balloon.
Glue some pennies to it.
Now blow up the balloon.
The pennies move away from each other (just like galaxies in the universe).
But the pennies themselves do not expand. Why not?
Because the cohesive forces within the penny easily overcome the expansive force of the balloon.

 

[phinds]

I always go back to the "pennies on a balloon" analogy.

Take a half-filled balloon.
Glue some pennies to it.
Now blow up the balloon.
The pennies move away from each other (just like galaxies in the universe).
But the pennies themselves do not expand. Why not?
Because the cohesive forces within the penny easily overcome the expansive force of the balloon.

See post #5

 

[Chalnoth]

I'm pretty sure this answer is not known but it always good to double check. Dark energy causes space to expand but the space inside a galaxy does not. Does anyone know why? I'm pretty sure the answer is not known, so I have a guess as to why this might be the case. Particles send out gravitational waves that cause the space around them to attract other particles. When these particles are not present the space is free of this attraction and will therefore expand. In brief, where there are massive objects space contracts or at least does not expand, where there are no massive objects space expands. Not much of an explanation but it's just a conjecture anyway.

Well, perhaps the simplest way of describing it is simply to point out that if you have a galaxy sitting in space with nothing around it, it stays stable due to the self-gravity of the stuff that makes up the galaxy. This fact doesn't change when you place the galaxy in an expanding universe, because the gravity of all the other objects in the universe has no net effect on the galaxy.

In fact, if you go through and carefully calculate what gravity says will happen in an expanding universe where some parts of the universe are more dense than others, you find that the more dense regions become stable while the less dense regions continue expanding. The exact same laws of gravity that govern the expansion say that more dense regions don't expand at all.

 

[Mark M]

No, dark energy does not cause space to expand. That's a general relativistic effect caused by an even distribution of matter. The solution of the Einstein Field Equations that is homogeneous and expanding is the FRW metric. However, the FRW metric only applies for homogeneous distributions of matter, which a galaxy is not. Instead, the Schwarzschild metric is used inside of a galaxy, where space isn't expanding.

Dark energy is a different business. It exerts a force at every point in space, just like a vacuum energy (it may or may not be that). It also ha the effect of being a negative pressure. That thing about homogeneous negative pressures is that they 'pile on' to whatever the universe is already doing. If the universe is expanding, dark energy will accelerate it. If it's contracting, it'll accelerate that too.

So, it has an extremely small presence inside of galaxies, although really negligible because of how weak it is.

 

[g.lemaitre]

Dark energy is a different business. It exerts a force at every point in space, just like a vacuum energy (it may or may not be that). It also ha the effect of being a negative pressure. ... If the universe is expanding, dark energy will accelerate it. If it's contracting, it'll accelerate that too.
.

well if dark energy causes the expansion to accelerate, what causes the expansion in the first place? i read in a textbook once that the answer is not know as to what causes space to expand.

 

[Mark M]

well if dark energy causes the expansion to accelerate, what causes the expansion in the first place? i read in a textbook once that the answer is not know as to what causes space to expand.

I mentioned it at the beginning of my post. Any homogenous arrangement of matter causes space to expand in general relativity.

 

[Chalnoth]

well if dark energy causes the expansion to accelerate, what causes the expansion in the first place? i read in a textbook once that the answer is not know as to what causes space to expand.

This is down to the initial conditions of our universe. We don't yet know how those initial conditions were set up. There are models, but this is still under investigation. And it is, unfortunately, probably going to be very difficult to get a handle of how the initial conditions for our universe were set up.

 

[bcrowell]

This may be of interest: http://www.lightandmatter.com/html_books/genrel/ch08/ch08.html#Section8.2 (subsection 8.2.6).

If absolutely everything expanded at the same rate (atoms, rulers, galaxies, separations between superclusters), then the expansion would be undetectable.

Actually, bound systems like galaxies and solar systems do expand a little -- just not very much. Numerical examples are given in the link, with references to papers.

 

[DaveC426913]

See post #5

The article describes the larger effect of pennies moving away from each other, but doesn't really draw an analogy to the pennies themselves not expanding - as an analogy to why galaxies do not expand. Perhaps the article could add something like that.

 

[Chronos]

Actually, as Ben noted, even gravitationally bound systems are slightly affected affected by expansion.

 

[Chalnoth]

Actually, as Ben noted, even gravitationally bound systems are slightly affected affected by expansion.

They're slightly affected by dark energy. But bound systems are indeed stable in an expanding universe. The rate of expansion determines how easily systems can become bound systems, however.

 

[Naty1]

Good recent discussion here:

Expanding Universe here?
https://www.physicsforums.com/showthread.php?t=619988&page=2

 

[bcrowell]

But bound systems are indeed stable in an expanding universe. The rate of expansion determines how easily systems can become bound systems, however.

The question isn't whether they're stable, it's whether they expand. The answer is that they do, but only slightly. The link I gave at #14 has footnotes to references, the most relevant being this: http://arxiv.org/abs/astro-ph/9803097v1

 

[Naty1]

bapowell:

The question isn't whether they're stable, it's whether they expand. The answer is that they do, but only slightly.

Not sure what 'expand' means in the stated context, but it seems different than this:

In another thread Wallace, of these forums says:
Post #63, thread # 162727:

….the 'expansion' (which we both definitely agree is a bad term for it!) is a result of the FRW metric, in particular a(t). The metric in the region of bound structure looks nothing like the FRW metric, in particular it has no global time dependence (though will of course evolve). For this reason I stand by the statement that the FRW metric is not valid on scales which are significantly inhomogeneous, since the metric has no component that reflects the global a(t), and hence the FRW picture does not relate to the dynamics of the system.QUOTE]

Anybody know how 'a' 'evolves' in a bound system??

By 'stable' do you different posters mean an orbit may have expanded by a smidgen, but once it does, an orbit remains fixed and independent of accelerated expansion?? If so, when did it expand and why does it no longer evolve with a??.

 

[Chalnoth]

The question isn't whether they're stable, it's whether they expand. The answer is that they do, but only slightly. The link I gave at #14 has footnotes to references, the most relevant being this: http://arxiv.org/abs/astro-ph/9803097v1

I don't think this can be correct. It seems to me that this paper simply assuming an acceleration based upon the overall expansion rate. This might be the right thing to do in the case of an overdense region overlaid on top of an expanding background. But this isn't the case: the overdense region itself makes up the entirety of the matter in that region, and does not rest on top of any sort of expanding background. The expansion that is occurring is occurring to far-away objects.

Since the expansion is occurring to far-away objects, and those objects are nearly symmetrical compared to any local object (due to the overall homogeneity and isotropy of the universe), Gauss's law guarantees that the motion of the far-away objects just can't have any impact on local systems.

One might argue that this must break down when we start to consider systems that are large compared to the horizon, but then we're either not talking about a universe that is expanding on average, or our large system hasn't captured all of the local matter and is sitting on top of an expanding background.

 

[Naty1]

Chalnoth:

It seems to me that this paper simply assuming an acceleration based upon the overall expansion rate.

I agree; One has to wonder.

These calculations are necessarily based on assumptions...the issue in all of them is whether the assumptions are accurate to the tolerances of calculation, say the radius of an atom relative to the distances in a solar system, for example. I have my doubts.

from the paper,

The purpose of the present paper is to provide a clear quantitative answer to the
problem. The motion of a particle subject to external forces in the (approximate) LIF
using Fermi normal coordinates is analyzed...

'approximate'...? Fermi normal typically utilizes eucledean tensor metric? what does that imply??

In this section,{3} the order of magnitude of the effect created by the cosmic expansion on the dynamics of local systems is estimated.

Order of magnitude! Do the assumptions support this??

The paper goes on to point out the accleration of the Earth solar acceleration overwhelms the cosmological acceleration by 44 orders of magnitude...while acceleration on the galactic scale overwhlems the cosmological acceleration by 7 orders.

The effects of the expansion of the universe on the dynamics of local systems are exemplified by the corrections induced in the two–body problem.

and they go on the make corrections based on TWO BODIES!

Then state

...the 3–dimensional equations of motion of a particle are
not coordinate–invariant and, like the equations of motion themselves, the correction
due to the cosmic expansion is dependent upon the frame employed. In this section,
we apply the results obtained in Sec. 2 to compute the perturbations of the two–body
problem in the LIF in an expanding, matter–dominated Einstein–de Sitter universe.For
simplicity, we restrict ourselves to the case of circular orbits...

two bodies...matter dominated? LIF? Are any realistic??

As always, that math is what it is...It is the assumptions that are fundamental to the outcome conclusions and without sensitivity analyses as to the effects of the assumptions, call me doubtful.

I have posted before the basic explanation given above by MarkM...and I believe supported by our own Wallace...and still have conceptual difficulty getting beyond it:

"dark energy...That's a general relativistic effect caused by an even distribution of matter. The solution of the Einstein Field Equations that is homogeneous and expanding is the FRW metric. However, the FRW metric only applies for homogeneous distributions of matter, which a galaxy is not. Instead, the Schwarzschild metric is used inside of a galaxy, where space isn't expanding."

 

[phinds]

The article describes the larger effect of pennies moving away from each other, but doesn't really draw an analogy to the pennies themselves not expanding - as an analogy to why galaxies do not expand. Perhaps the article could add something like that.

Dave, I thought this:

THIRD: LOCAL EFFECTS The pennies don't change size (gravitationally bound systems don't expand and nothing inside of them expands), they just get farther apart and none of them are at the center.

was enough, no?

Anyway this whole thread, and another similar one, now have me to the point of believing that there is no consensus as to whether there IS any expansion of gravitationally bound systems. I previously believed that that there was not, was recently convinced there is, and now just believe that there is no consensus --- there may or may not be (any expansion).

I realize that science is not done by consensus. Einstein once replied, when told that there was a pamphlet out with 100 authors contending that he was wrong, "Why 100? If I were wrong, one would have been enough."

My point is that knowledgeable folks are making definitive statements on both sides of the question which leaves an amateur like me floundering.

EDIT: I understand that even those who argue that there IS expansion inside galaxies say that it is negligible, so the engineer in me says it really doesn't matter (and it doesn't in practical terms), but the amateur physicist in me says negligible and zero are radically different, so it matters a lot.

 

[Lino]

...Anyway this whole thread, and another similar one, now have me to the point of believing that there is no consensus as to whether there IS any expansion of gravitationally bound systems. I previously believed that that there was not, was recently convinced there is, and now just believe that there is no consensus --- there may or may not be...

Phinds, I might be able to shed some light on the seeming lack of consensus but am completely open to correction. Using the rubber sheet analogy, with the large weight in the centre, roll a smaller ball onto the sheet and watch it get gravitationally captured and orbit the large weight. Remove the small ball, stretch the sheet further and roll the ball back onto the sheet. The extra stretch, changes (reduces) the curvature of the sheet, and the orbit is further from the centre.

The extra (continuous) stretch is analogous to (continuous) expansion, but the only effect is a one-off impact on the location of the orbit. Apply it to a gravitationally bound system, for exampsle the sun / earth, and the orbit is slightly greater than if there was no expansion (of space), but that is a one-off effect and there is no further change to the size of the system.

So (IMHO), the various answers depend on the question being asked:
* Is space in a gravitationally bound system expanding? Yes.
* Does this have an impact on the system? Yes, but it is very, very small and one-off.
* Is the size of the system growing (with expansion)? No.

But given that I am only a junior-trainee-amateur, I am open to correction.

Regards,

Noel.

 

[andrewkirk]

If absolutely everything expanded at the same rate (atoms, rulers, galaxies, separations between superclusters), then the expansion would be undetectable.

What about the relationship of redshift to radial distance? Wouldn't that still be observable and hence provide a pointer towards expansion? Or would we no longer be able to tell how distant the things we were observing were, and hence not be able to infer the Hubble relation?

 

[Chalnoth]

So (IMHO), the various answers depend on the question being asked:
* Is space in a gravitationally bound system expanding? Yes.

No, it isn't. I'm reasonably certain that this has been experimentally demonstrated using laser ranging experiments, though my Google-fu is failing me at the moment.

The calculations that result in some expansion basically assume the expansion. They don't derive it.

 

[andrewkirk]

If the expansion comes from a nonzero cosmological constant $\Lambda$ then the answer to the question is quite clear - the configuration of stars within a galaxy will be very slightly different from what it would be if $\Lambda=0$. One would intuitively expect that difference to be that the radius of the galaxy stabilises at a slightly larger distance than would occur if $\Lambda=0$. But it may be that with some peculiar-shaped galaxies that does not occur, because of the way interactions play out under the field equations.

But in every case, the configuration of stars in the galaxy will be determined by Einstein's Field Equation $G+g\Lambda=T$, which operates everywhere in spacetime, so it must be the case that a nonzero $\Lambda$ changes things.

If cosmological expansion is instead caused by something that is not constant, such as quintessence or moduli, the answer is 'who knows'. These fields vary over time and space so their effect within a galaxy will depend on the strength and configuration of the field within that galaxy.

 

[Mark M]

"dark energy...That's a general relativistic effect caused by an even distribution of matter. The solution of the Einstein Field Equations that is homogeneous and expanding is the FRW metric. However, the FRW metric only applies for homogeneous distributions of matter, which a galaxy is not. Instead, the Schwarzschild metric is used inside of a galaxy, where space isn't expanding."

Naty, the part you left out was important. Normal expansion is an effect of general relativity, not dark energy. Dark energy 'piles on' and accelerates the normal, general relativistic expansion of the FRW metric. Normal expansion is a feature of the FRW metric, whereas dark energy is a constant force you must factor in.

That's why I stand by what I said in that thread. Normal expansion due to the FRW metric applies only to intergalactic space. However, dark energy has a slight effect inside of galaxies. That's because it's included in the Einstein field equations in the form of a cosmological constant. The EFE govern gravitational interactions everywhere, so we can naturally conclude that dark energy has a slight effect everywhere.

 

[Naty1]

MarkM:

Normal expansion due to the FRW metric applies only to intergalactic space. However, dark energy has a slight effect inside of galaxies.

Yes, in general I like that explanation and above all it IS logical. And two guys here I respect seemed to agree in another thread...

But I also keep an open mind because I don't understand how 'a' evolves within a
gravitationally bound system and am not sufficiently conversant in all the mathematical assumptions to know what models apply and what ones weaken at such miniscule calculational distances:

When Wallace says emphatically:

...The metric in the region of bound structure looks nothing like the FRW metric, in particular it has no global time dependence (though will of course evolve).

...I have to wonder about the effect.
Wallace is apparently a practicing cosmologist so I put considerable weight when he make a strong point as in that quote.

and I like phinds comment:

...but the amateur physicist in me says negligible and zero are radically different, so it matters a lot.

 

[andrewkirk]

I don't understand how 'a' evolves within a gravitationally bound system

This question has no answer because 'a(t)' is a parameter of the FLRW model, which does not apply within a bound system such as a galaxy. Asking what the FLRW 'a' is inside a galaxy would be like asking what is the radius of an ellipse.

The FLRW model assumes perfect homogeneity of the universe, but a galaxy is by definition a region in which the homogeneity assumption does not apply.

The question we can ask, that does make sense within a galaxy, is:

'What effect do the factors that make the universe's expansion accelerate have within a galaxy?'

The answer to that is most likely reached via analysis of the impact of a nonzero $\Lambda$ on the curvature of spacetime within a galaxy. My facility with tensor equations is regrettably way below the level necessary to answer that question. But it seems reasonable to be confident that the answer is not 'none whatsoever'.

 

[Chalnoth]

This question has no answer because 'a(t)' is a parameter of the FLRW model, which does not apply within a bound system such as a galaxy. Asking what the FLRW 'a' is inside a galaxy would be like asking what is the radius of an ellipse.

The FLRW model assumes perfect homogeneity of the universe, but a galaxy is by definition a region in which the homogeneity assumption does not apply.

The question we can ask, that does make sense within a galaxy, is:

'What effect do the factors that make the universe's expansion accelerate have within a galaxy?'

The answer to that is most likely reached via analysis of the impact of a nonzero $\Lambda$ on the curvature of spacetime within a galaxy. My facility with tensor equations is regrettably way below the level necessary to answer that question. But it seems reasonable to be confident that the answer is not 'none whatsoever'.

Oh, yeah, the effect of dark energy on galaxies is most definitely not zero. It's small, but not zero. The effect is even measurable for large galaxy clusters:
http://en.wikipedia.org/wiki/Sachs–Wolfe_effect