More extended equilibrium configurations due to dark energy?

[Suekdccia]

TL;DR Summary

More extended equilibrium configurations due to dark energy?

Dark Energy puts a constrain on the size of overdensities (like clusters and superclusters of galaxies) and their growth.

A higher Dark Energy density would reduce the radius of the zone where matter would be gravitationally bound, because more Dark Energy density would mean that objects would have it easier to escape to infinity as they are futher apart from the gravitational source.

However, can Dark Energy cause these systems to be more extended (even if by a tiny fraction) inside the zone where they are still bound (especially in the outskirts of the systems, near the limit radius distance where Dark Energy begins to make objects recede and escape to infinity)?

I ask this after reading this paper (https://arxiv.org/abs/1404.7744) where authors say that in the presence of Dark Energy the equilibrium configuration of overdensities would be more extended in radius

I mean, in a universe without Dark Energy, these structures could grow indefinetely because objects would not recede to infinity due to the accelerated expansion of spacetime. In that sense, these systems would be bigger in that universe. In the presence of Dark Energy overdensities could only grow up to the radius where matter would recede to infinity, but within the bound system, would it be a bit more extended in size (meaning that matter would be a bit more separated) than in a universe without Dark Energy?

 

[PeterDonis]

within the bound system, would it be a bit more extended in size (meaning that matter would be a bit more separated) than in a universe without Dark Energy?

To answer this question, you have to ask what "the bound system" means. In the paper you link to, it appears that it means "the same matter", i.e., the same galaxies, stars, etc--ultimately that comes down to the same quantity of elementary particles in the same arrangements. If that is held constant, and if we assume that the quantity of matter is small enough that the bound system is within the size limit imposed by dark energy, then yes, the bound system will be larger in size, i.e., less tightly bound, in the presence of dark energy than without it.

 

[Suekdccia]

To answer this question, you have to ask what "the bound system" means. In the paper you link to, it appears that it means "the same matter", i.e., the same galaxies, stars, etc--ultimately that comes down to the same quantity of elementary particles in the same arrangements. If that is held constant, and if we assume that the quantity of matter is small enough that the bound system is within the size limit imposed by dark energy, then yes, the bound system will be larger in size, i.e., less tightly bound, in the presence of dark energy than without it.

Thank you. Would this mean that if there are orbits of bodies that are sufficiently far apart from each other (but inside the bound system), the orbital radius would be larger?

Also, I was reading a bit more about these scenarios with dark energy and I had a few questions that I think you could help me with

1. In this long discussion (https://www.physicsforums.com/threa...gical-constant-any-problems-with-that.945305/) related to the tethered galaxy problem, you said that if we attached a couple of galaxies with a rope we could only extract the energy resulting from the tension. But if we let the rope loose in one galaxy (running through a hypothetical generator) it would run because the other galaxy would be receding again due to the accelerated expansion of the universe. This would supposedly continue until the galaxy reaches the event horizon, where the rope would break. Then, wouldn't we have extracted an energy equivalent to the rest mass of the galaxy (ignoring other problems like redshifting)?

2. Also, in this other post (https://www.physicsforums.com/threads/what-is-the-acceleration-of-expanding-space.934316/) you talk about "tidal gravity" caused by dark energy. Could dark energy then (at least indirectly) cause some kind of tidal force in some cases (like in filaments connecting different clusters of galaxies)? Or if tidal gravity is not tidal force exactly, would it cause some kind of stress (like it happens with tidal forces per se)?

 

[PeterDonis]

Would this mean that if there are orbits of bodies that are sufficiently far apart from each other (but inside the bound system), the orbital radius would be larger?

Isn't that what the size of the bound system means?

 

[PeterDonis]

you talk about "tidal gravity" caused by dark energy

Only in the general sense of "spacetime curvature". The curvature caused by dark energy is entirely Ricci curvature (negative Ricci curvature, so objects on geodesic trajectories accelerate away from each other instead of towards each other). The usual layman's sense of "tidal gravity", such as the tides on the Earth caused by the Moon, is Weyl curvature, not Ricci curvature. Dark energy does not cause any Weyl curvature, so it won't produce phenomena like the tides on the Earth caused by the Moon.

 

[PeterDonis]

f tidal gravity is not tidal force exactly, would it cause some kind of stress

An object immersed in dark energy that maintains its size (for example by inter-atomic bonds) will, in principle, be under nonzero stress because of the dark energy (instead of being under zero stress as it would be if it were in flat spacetime). However, for any ordinary object this effect is many, many orders of magnitude too small to measure.

 

[PeterDonis]

if we let the rope loose in one galaxy (running through a hypothetical generator) it would run because the other galaxy would be receding again due to the accelerated expansion of the universe

Not if there is tension in the cable--which there has to be to extract energy. If there is tension in the cable, then, as I noted in the thread, the two galaxies are one object, and the tension in the cable is what enables the object to maintain its size in the presence of dark energy--just like the inter-atomic bonds I referred to in post #6 just now. If you allow the galaxies to recede from each other, you are releasing the tension in the cable, and you can only do that once.

This would supposedly continue until the galaxy reaches the event horizon, where the rope would break. Then, wouldn't we have extracted an energy equivalent to the rest mass of the galaxy (ignoring other problems like redshifting)?

It looks like you are making analogy with slowly lowering an object towards the horizon of a black hole and extracting energy that way. But you are missing a crucial part of the latter scenario: the platform you are lowering the object from is not in free fall. It has to be suspended at some constant altitude above the hole, for example by rockets. If you let the platform free fall, you can't extract energy by slowly lowering an object from it.

In the tethered galaxy case, the galaxy you are extending the rope from, and where you want to run a generator, is in free fall, so you can't extract energy by slowly lowering a second object (the other galaxy) from it. You would have to have a static platform that was suspended at some constant altitude above the cosmological horizon.

 

[PeterDonis]

You would have to have a static platform that was suspended at some constant altitude above the cosmological horizon.

And note that even in that case, the "slow lowering" process doesn't work exactly the same as for the black hole case. Hint: look at the potential energy (or, equivalently, the redshift factor) in static coordinates on de Sitter spacetime, as a function of the radial coordinate $r$.

 

[Suekdccia]

Isn't that what the size of the bound system means?

I was just trying to confirm

 

[Suekdccia]

Not if there is tension in the cable--which there has to be to extract energy. If there is tension in the cable, then, as I noted in the thread, the two galaxies are one object, and the tension in the cable is what enables the object to maintain its size in the presence of dark energy--just like the inter-atomic bonds I referred to in post #6 just now. If you allow the galaxies to recede from each other, you are releasing the tension in the cable, and you can only do that once.It looks like you are making analogy with slowly lowering an object towards the horizon of a black hole and extracting energy that way. But you are missing a crucial part of the latter scenario: the platform you are lowering the object from is not in free fall. It has to be suspended at some constant altitude above the hole, for example by rockets. If you let the platform free fall, you can't extract energy by slowly lowering an object from it.

In the tethered galaxy case, the galaxy you are extending the rope from, and where you want to run a generator, is in free fall, so you can't extract energy by slowly lowering a second object (the other galaxy) from it. You would have to have a static platform that was suspended at some constant altitude above the cosmological horizon.

Mmmmh but in that case, would these papers be totally wrong?

https://arxiv.org/abs/astro-ph/0104349

https://arxiv.org/abs/1911.08726

https://ui.adsabs.harvard.edu/abs/1995ApJ...446...63H/abstractI mean, how couldn't the authors of these papers overlook that detail?

 

[Suekdccia]

However, for any ordinary object this effect is many, many orders of magnitude too small to measure.

What about bigger objects (like very big galaxies or clusters)? Would there be some kind of stress then?

 

[PeterDonis]

would these papers be totally wrong?

As far as I can tell, these papers, to the extent they are talking about energy extraction (note that the first paper, as far as I can tell, does not discuss this at all--it talks about what happens if you let the tethered galaxy go so it moves freely, i.e., geodesically, and obviously you can't extract any energy in that case), are talking about the static case I described previously, where something is holding the platform where the energy extraction is taking place steady.

That said, there is one loophole in the de Sitter case, which is discussed towards the end of the previous thread you linked to: if you have your platform following an appropriate comoving worldline in de Sitter spacetime, and you extend cables out in two opposite directions from the object, then by properly balancing the cable payout on both sides, you can treat your platform as if it were static. In that particular edge case, yes, I think you could extract energy from both cables by a slow lowering process similar to that for the black hole case. But the balancing of two opposite cables is crucial to this plan.

 

[PeterDonis]

What about bigger objects (like very big galaxies or clusters)? Would there be some kind of stress then?

How would you have stress in galaxies or clusters? There is no analogue of "inter-atomic forces" there; all of the stars are following geodesic orbits.

 

[Suekdccia]

As far as I can tell, these papers, to the extent they are talking about energy extraction (note that the first paper, as far as I can tell, does not discuss this at all--it talks about what happens if you let the tethered galaxy go so it moves freely, i.e., geodesically, and obviously you can't extract any energy in that case), are talking about the static case I described previously, where something is holding the platform where the energy extraction is taking place steady.

That said, there is one loophole in the de Sitter case, which is discussed towards the end of the previous thread you linked to: if you have your platform following an appropriate comoving worldline in de Sitter spacetime, and you extend cables out in two opposite directions from the object, then by properly balancing the cable payout on both sides, you can treat your platform as if it were static. In that particular edge case, yes, I think you could extract energy from both cables by a slow lowering process similar to that for the black hole case. But the balancing of two opposite cables is crucial to this plan.

I see...

Would that scenario you describe be applied to a universe that is approaching deSitter space but is not yet one (such as our universe)?

 

[Suekdccia]

How would you have stress in galaxies or clusters? There is no analogue of "inter-atomic forces" there; all of the stars are following geodesic orbits.

I thought that perhaps gravity and tidal forces could be some kind of analogues to the forces binding atoms

 

[PeterDonis]

Would that scenario you describe be applied to a universe that is approaching deSitter space but is not yet one (such as our universe)?

In general, yes, but the amount of energy extractable would be less, because the effects of the ordinary matter would to some extent counteract the effects of the dark energy.

 

[PeterDonis]

I thought that perhaps gravity and tidal forces could be some kind of analogues to the forces binding atoms

No, because these aren't forces in GR. The term "tidal forces", strictly speaking, does not mean the effects of spacetime curvature on geodesics. It means the non-gravitational forces inside objects that resist the effects of spacetime curvature and cause individual atoms inside the object to not travel on geodesic paths.

 

[Suekdccia]

In general, yes, but the amount of energy extractable would be less, because the effects of the ordinary matter would to some extent counteract the effects of the dark energy.

It would counteract it by gravity itself, I suppose (which has the opposite effect of dark energy)

 

[Suekdccia]

No, because these aren't forces in GR. The term "tidal forces", strictly speaking, does not mean the effects of spacetime curvature on geodesics. It means the non-gravitational forces inside objects that resist the effects of spacetime curvature and cause individual atoms inside the object to not travel on geodesic paths.

Mmmh and how about dark energy causing tidal forces indirectly (if that makes sense).

I mean, although the density of dark energy is the same throughout the universe, some parts of it expand faster than others. For example, cosmic voids, as their matter density is very low, expand faster while overdensities of matter would do it slower. Wouldn't this asymmetry in a system and its environment exert a tidal influence, meaning that gravitational forces are different in different directions?. This would cause the system to expand at a different rate in different directions, resulting in structures like filaments and sheets in the large-scale structure of the universe. And this would be indirectly caused by dark energy (also by gravity, but there would be some contribution from dark energy). Therefore, wouldn't filaments and sheets experience tidal forces within them, that would be indirectly caused by dark energy?

 

[PeterDonis]

It would counteract it by gravity itself, I suppose (which has the opposite effect of dark energy)

More precisely, the Ricci curvature due to the ordinary matter cancels out a portion of the Ricci curvature due to dark energy.

although the density of dark energy is the same throughout the universe, some parts of it expand faster than others

No, they don't. The dark energy density is constant in time as well as in space. The difference in expansion you talk about, due to overdensities or underdensities in ordinary matter, does not affect dark energy at all. It only affects the distribution of ordinary matter.