Dark Galaxy Discovered: Unbelievable Findings

[SpaceTiger]

Let's create a universe with only two very small masses. Let's say they are bits of dark matter. Let's create a galaxy of these two bits by placing them in orbit around one another at a fixed distance.

Let's introduce a very weak antigravity force, we'll call "dark energy." This force is wa-a-a-a-ay weaker than gravity by many orders of magnitude, though like gravity it works on all scales (since it pushes on all matter). How might it effect our universe model?

Ok, I think this is a good example. I'll repeat your assumptions in a different way, since they will be crucial to the arguments that follow:

1) The "repulsive force" is very weak on the scale of the system. It will eventually dominate the potential if one goes to large enough radii, but it will be many orders of magnitude larger than the separation between the masses.
2) The potential is time-independent; that is, the energy density of dark energy at a particular location in space does not change with time. Since we're talking about the cosmological constant, not some other form of dark energy, this is a required assumption.

Since we've established a time-independent potential, we can define an energy for the orbiting mass.

E=-V_g(r)+V_r(r)+T

where V_g is the potential due to gravity (the usual 1/r potential), V_r is the potential of the "repulsive" force, and T is the total kinetic energy of the orbiting body. The radial coordinate is measured from the center of mass of the orbiting bodies. I've pulled the minus sign out of the gravitational potential to make its attractive nature explicit. For the arguments that follow, it won't matter if the repulsive potential increases or decreases with radius, as long as it stays well below the magnitude of the gravitational potential.

Let's start by considering a purely radial orbit. In this case, the kinetic energy is just:

T=\frac{1}{2}mv_r^2

Now, the question is, can we create an orbit that is bound for all time? To answer this, let's just choose some initial condition. We don't have to think very hard on this one, let's just drop the object from some radius, r. That is, v_r=0 at r=r_0. What is the total energy of the object? To answer that, we just set the kinetic energy to zero:

E_{tot}=-V_g(r_0)+V_r(r_0)

A bound orbit has negative total energy and an unbound one has positive. Since we agreed that V_r(r_0) is much less than the gravitational potential, this orbit must be bound. Since the potential is time-independent, energy conservation must always apply and the orbit must be forever bound.

We can also examine circular orbits. You seem to claim that they would be unstable in this potential, but we can examine this directly. Setting v_r=0, the energy is given by:

E=-\frac{GMm}{r}+V_r(r)+\frac{L^2}{2mr^2}=V_{eff}

A circular orbit is found by finding the minima and maxima of the effective potential as a function of r. The stability is determined by concavity and positive concavity means a stable orbit. Now we could solve for the first and second derivatives of this function and get explicit answers, but it should be easier to just imagine the shape of the function. In a Newtonian potential, if L is small enough, the function should look something like the red curve in this picture:

http://qonos.princeton.edu/nbond/Kepler78.gif

Disregard the blue curve, as it's not relevant here. As you can see, there's a stable circular orbit in the red curve at x=1. The question we want to now ask is whether or not this changes qualitatively when we add a small potential with positive sign; that is, does this potential change the shape of the curve? If it's very weak, I don't see how it could. You can imagine adding a very small number to every point on that curve, all it will do is shift the minimum slightly.

So what does this mean? Basically, it means that there are stable circular orbits in the presence of a cosmological constant. The dark energy does not forever push the objects apart. All of these arguments fall apart if the dark energy density is increasing with time because the potential becomes time-dependent and energy is not conserved. This, again, is the Big Rip.

Obviously (to me) this energy/force (regardless of how small) would tend to spread our two bits apart. Why? Because even if it is very weak, a little bit of it is inbetween the two separate but orbitting bits. They are pushed apart (however slightly). Then, since there's more space, more DE get's inbetween and pushes them apart more effectively. then more DE gets inbetween and again pushes them apart even more effectively, then... you get the idea. Now extrapolate this effect as having been happening for about 10 billion years, each orbit being slightly larger than the last.

You can analyze this same problem by summing the effect of an infinite number of infinitesimal forces, but you'll get the same answer. The series must, at some point, converge. If it didn't, energy and/or angular momentum would not be conserved.

However, DE could never be strong enough in this model to separate single gravitational bodies as there is no room to work and insufficient angular momentum to nullify the great strength of gravity (not to mention electro-static attraction). It's only the equalizing force of angular momentum that would allow a condition of balance that can be disturbed by the DE.

If you were to take an orbit in a Newtonian potential and then suddenly introduce a field of dark energy, you would get a perturbation in the orbit for the reasons you give. However, the orbit will quickly reach a new equilibrium that includes the effects of the dark energy (that is, the three forces will come to a balance). If you don't further change your system, it will remain in this equilibrium for all time.

 

[ubavontuba]

Ok, I think this is a good example. I'll repeat your assumptions in a different way, since they will be crucial to the arguments that follow:

1) The "repulsive force" is very weak on the scale of the system. It will eventually dominate the potential if one goes to large enough radii, but it will be many orders of magnitude larger than the separation between the masses.
2) The potential is time-independent; that is, the energy density of dark energy at a particular location in space does not change with time. Since we're talking about the cosmological constant, not some other form of dark energy, this is a required assumption.

Hmm, as I understand it (I may be mistaken), the dark energy in our universe is possibly time-dependent in that it apparently started fairly late in the cosmic evolution.

Since we've established a time-independent potential, we can define an energy for the orbiting mass.

E=-V_g(r)+V_r(r)+T

where V_g is the potential due to gravity (the usual 1/r potential), V_r is the potential of the "repulsive" force, and T is the total kinetic energy of the orbiting body. The radial coordinate is measured from the center of mass of the orbiting bodies. I've pulled the minus sign out of the gravitational potential to make its attractive nature explicit. For the arguments that follow, it won't matter if the repulsive potential increases or decreases with radius, as long as it stays well below the magnitude of the gravitational potential.

Let's start by considering a purely radial orbit. In this case, the kinetic energy is just:

T=\frac{1}{2}mv_r^2

Now, the question is, can we create an orbit that is bound for all time? To answer this, let's just choose some initial condition. We don't have to think very hard on this one, let's just drop the object from some radius, r. That is, v_r=0 at r=r_0. What is the total energy of the object? To answer that, we just set the kinetic energy to zero:

E_{tot}=-V_g(r_0)+V_r(r_0)

A bound orbit has negative total energy and an unbound one has positive. Since we agreed that V_r(r_0) is much less than the gravitational potential, this orbit must be bound. Since the potential is time-independent, energy conservation must always apply and the orbit must be forever bound.

Actually, (so I've read) it seems apparent that dark energy might be a violation of conservation.

We can also examine circular orbits. You seem to claim that they would be unstable in this potential, but we can examine this directly. Setting v_r=0, the energy is given by:

E=-\frac{GMm}{r}+V_r(r)+\frac{L^2}{2mr^2}=V_{eff}

A circular orbit is found by finding the minima and maxima of the effective potential as a function of r. The stability is determined by concavity and positive concavity means a stable orbit. Now we could solve for the first and second derivatives of this function and get explicit answers, but it should be easier to just imagine the shape of the function. In a Newtonian potential, if L is small enough, the function should look something like the red curve in this picture:

http://qonos.princeton.edu/nbond/Kepler78.gif

Disregard the blue curve, as it's not relevant here. As you can see, there's a stable circular orbit in the red curve at x=1. The question we want to now ask is whether or not this changes qualitatively when we add a small potential with positive sign; that is, does this potential change the shape of the curve? If it's very weak, I don't see how it could. You can imagine adding a very small number to every point on that curve, all it will do is shift the minimum slightly.

Ah, but this "very small number" grows with distance. Shifting the curve will require you to reshift the curve for the new values and then you'll have to reshift the curve...

So what does this mean? Basically, it means that there are stable circular orbits in the presence of a cosmological constant. The dark energy does not forever push the objects apart. All of these arguments fall apart if the dark energy density is increasing with time because the potential becomes time-dependent and energy is not conserved. This, again, is the Big Rip.

Or, they move apart as the dark energy potential is increasing with distance and gravity potential is decreasing with distance. Conservation (in this case) is not firmly established. Perhaps there is an asymmetry to it that we are too small to perceive, perhaps there is a super-symmetry of multiverses that allows this apparent asymmetry to occur in our universe. Perhaps all of DE is symmetrically equivalent to all of gravity, Who knows?

You can analyze this same problem by summing the effect of an infinite number of infinitesimal forces, but you'll get the same answer. The series must, at some point, converge. If it didn't, energy and/or angular momentum would not be conserved.

Right. But conservation is questionable on large scales, the CP(T?) violation being one example.

If you were to take an orbit in a Newtonian potential and then suddenly introduce a field of dark energy, you would get a perturbation in the orbit for the reasons you give. However, the orbit will quickly reach a new equilibrium that includes the effects of the dark energy (that is, the three forces will come to a balance). If you don't further change your system, it will remain in this equilibrium for all time.

Right, but the changes wrought by DE create changes to DE and gravity potential that then cause changes to the system that then change DE and gravity potential that then... It's a vicious circle.

Conservation of momentum appears to create a convergence in your fixed DE value system, but it doesn't when one considers the gravitational potential between the two bodies also changes with distance. There shouldn't be an acceleration in a changeless potential (as you would have it), but the potential does change, even if DE potential doesn't. This is due to the inverse square law applicable to gravity potential. The orbits should steadily increase in circumference in an acceleration, should the potential of DE remain unchanged and the potential of gravity decrease with distance.

Obviously, this would be an excrutiatingly slow process of separation, but we have billions of years of its effects to observe. We should see "fuzzy," more dispersed galaxies (if it's a separating force, like space-time expansion). Or, we should see signs of compression (if it's a pushing force from between the galaxies (ZPE?)).

Does this make sense?

 

[SpaceTiger]

Hmm, as I understand it (I may be mistaken), the dark energy in our universe is possibly time-dependent in that it apparently started fairly late in the cosmic evolution.

It is possible that the dark energy has a time-dependent density, but that's not immediately derivable from its late-time dominance in the universe. If the dark energy density were constant with time, then you would get late-time dominance naturally by virtue of the fact that the matter density drops as the universe expands. The so-called "Lambda transition" occurs when the matter energy density drops to that of the cosmological constant.

The most popular theory of the universe right now is \Lambda CDM, where the \Lambda refers to the cosmological constant. There are other theories in which the dark energy density changes with time and in these models my arguments would not apply, as I've already said. Most of them actually have the density decreasing with time, meaning that the orbits should exhibit a slight contraction.

Actually, (so I've read) it seems apparent that dark energy might be a violation of conservation.

In fact, a fully general relativistic treatment of the universe does not conserve energy, even in the absence of the dark energy. However, as you said, we were working in the Newtonian approximation. With galaxies and weak fields, this approximation should be valid. There may be higher-order relativistic corrections, but they're small, difficult to model, and not in correspondence with the arguments you gave.

Ah, but this "very small number" grows with distance. Shifting the curve will require you to reshift the curve for the new values and then you'll have to reshift the curve...

The plot is already a function of distance (r). I think you should read the argument and plots again a little more carefully. The "shifting" of the plot is only done once with the addition of the dark energy potential (which is already a function of distance). The potential does not change with time.

Conservation (in this case) is not firmly established.

In your toy model, it's very firmly established. We can modify this toy model and speculate that higher-order general relativistic corrections might produce a change in one direction or the other, but it would be an even smaller shift than has already been produced.

Perhaps there is an asymmetry to it that we are too small to perceive, perhaps there is a super-symmetry of multiverses that allows this apparent asymmetry to occur in our universe. Perhaps all of DE is symmetrically equivalent to all of gravity, Who knows?

In the real world, there are all sorts of potential complications, but the purpose of simple models is to remove those and understand the physics one bit at a time. In the purely Newtonian approximation, along with the mass distribution you've postulated, energy will be conserved and the orbits can be bound.

Right. But conservation is questionable on large scales, the CP(T?) violation being one example.

Even GR is questionable on large scales -- it's very hard to test theories of gravity on cosmological scales unless they produce major deviations from GR.

Right, but the changes wrought by DE create changes to DE and gravity potential that then cause changes to the system that then change DE and gravity potential that then... It's a vicious circle.

I don't follow you here. Are you coupling Lagrangians?

Conservation of momentum appears to create a convergence in your fixed DE value system, but it doesn't when one considers the gravitational potential between the two bodies also changes with distance. There shouldn't be an acceleration in a changeless potential (as you would have it), but the potential does change, even if DE potential doesn't. This is due to the inverse square law applicable to gravity potential. The orbits should steadily increase in circumference in an acceleration, should the potential of DE remain unchanged and the potential of gravity decrease with distance.

I suspect you've completely misunderstood my argument. On the very first step, I give both the dark energy and gravitational potential a distance dependence.

Does this make sense?

I think we should try approaching this more methodically. Go through my arguments and make sure you understand each step. If you're confused about something in particular, ask me to elaborate. Have you ever taken a class or done problems on orbital dynamics?

 

[ubavontuba]

The plot is already a function of distance (r). I think you should read the argument and plots again a little more carefully. The "shifting" of the plot is only done once with the addition of the dark energy potential (which is already a function of distance). The potential does not change with time.

In your equation E_{tot}=-V_g(r_0)+V_r(r_0), it looks to me like you arbitrarily predetermined the outcome you wanted by supposing beforehand that there is such a stable orbit. I think you will find the distance for this orbit is zero for any non-zero mass.

I think we should try approaching this more methodically. Go through my arguments and make sure you understand each step. If you're confused about something in particular, ask me to elaborate. Have you ever taken a class or done problems on orbital dynamics?

I don't think I'm confused (yet), but I'll let you know if I feel that way. It's funny you should ask though. Another nickname of mine is "Uba confused," or "Uba confused Vontuba."

 

[SpaceTiger]

In your equation E_{tot}=-V_g(r_0)+V_r(r_0), it looks to me like you arbitrarily predetermined the outcome you wanted by supposing beforehand that there is such a stable orbit. I think you will find the distance for this orbit is zero for any non-zero mass.

That equation is the energy of a mass starting with zero velocity at r=r_0. It doesn't matter what the form of the potential is, as long as it's spherically symmetric (or, alternatively, one-dimensional), that equation will be valid. If it were true that V_r(r_0) > V_g(r_0), then the orbit would be unbound and the particle would be able to escape.

Think about it this way. A mass that is "free" will have only kinetic energy, which must be positive. If its total energy is negative at any point in the orbit, then conservation of energy demands that it never be "free".

 

[ubavontuba]

That equation is the energy of a mass starting with zero velocity at r=r_0. It doesn't matter what the form of the potential is, as long as it's spherically symmetric (or, alternatively, one-dimensional), that equation will be valid. If it were true that V_r(r_0) > V_g(r_0), then the orbit would be unbound and the particle would be able to escape.

Think about it this way. A mass that is "free" will have only kinetic energy, which must be positive. If its total energy is negative at any point in the orbit, then conservation of energy demands that it never be "free".

Hmm... Is it a one-dimensional consideration? Did you consider that in this model at r=r_0 the DE potential is zero but at any other given distance it is no longer zero?

 

[SpaceTiger]

Hmm... Is it a one-dimensional consideration? Did you consider that in this model at r=r_0 the DE potential is zero but at any other given distance it is no longer zero?

I'm allowing the DE potential to have any value at any radius, as long as its magnitude is much less than that of the gravitational potential. This approximation will break down eventually, but only at distances much larger than the separation of the objects (as stated in my assumptions).

 

[ubavontuba]

I'm allowing the DE potential to have any value at any radius, as long as its magnitude is much less than that of the gravitational potential. This approximation will break down eventually, but only at distances much larger than the separation of the objects (as stated in my assumptions).

Okay, let's go with this and I'll ask you these questions. Supposing you apply a reasonable figure for DE to galactic sized orbits, what happens? How big must the orbit be, to be adversely affected?

 

[SpaceTiger]

Supposing you apply a reasonable figure for DE to galactic sized orbits, what happens?

You mean a value for the cosmological constant? Reasonable values for the current cosmological model will have very little effect on galactic orbits. There be an extremely undetectable shift, but that's all.

How big must the orbit be, to be adversely affected?

About as big as a galaxy cluster (>~10 Mpc). We still can't measure the effect directly (yet), but it would have a non-negligible impact.

 

[ubavontuba]

Supposing you apply a reasonable figure for DE to galactic sized orbits, what happens?

You mean a value for the cosmological constant? Reasonable values for the current cosmological model will have very little effect on galactic orbits. There be an extremely undetectable shift, but that's all.

Aren't you essentially saying the facts fit the model without examining the facts?

How big must the orbit be, to be adversely affected?

About as big as a galaxy cluster (>~10 Mpc). We still can't measure the effect directly (yet), but it would have a non-negligible impact.

If there is this fine line in regards to galaxy cluster formation that essentially creates a demarcation line between gravity and DE, why do galaxy clusters come in so many different sizes and densities?

I feel I understand your DE orbital model, but have problems with it in accordance with dark matter (DM). As DE pushes orbits apart, angular momentum decreases faster than gravity decreases, therefore stability is achieved (albeit in a slightly higher orbit).

Modelling this on a large scale, it would seem that DE would tend to make orbits higher and slower. However, we observe galactic orbits to be too low and fast due to DM.

This just seems to be a kind of paradox to me. Since DM supposedly reacts with gravity, it should have this same high speed galactic rotation and therefore it should easily be pushed out by even the weakest DE.

The only way I see this working is if DM doesn't react with DE at all, but only with gravity. But like I said earlier, logic rules this out since it is obvious that DE reacts with gravitational mass and DM is purportedly a gravitational mass, therefore DE should react with DM. (I forget the name of this logic form).

See? It's not dark matter or dark energy individually as hypothesis that I have a problem with. It's that when you combine them in accordance with NM, they tend to look rather messy. Has anyone else noticed this? How do they explain these inconsistencies... MOND? (Where is Occam's razor when you need it?)

 

[Garth]

(Where is Occam's razor when you need it?)

Here - read my signature!

View attachment William of Ockham small.bmp
(Taken from a stained glass window in All Saints Church, Ockham, near where I live in Surrey. William was a fourteenth-century Scholastic philosopher, born at or near the village of Ockham)

In the standard model DE produces a small 'antigravity' force that is overwhelmed by normal gravitaiton at normal ranges but only becomes dominant at the largest scales when the average density, and hence normal gravitational forces, are small enough.

Garth

 

[ubavontuba]

Occam sock 'em robots!

In the standard model DE produces a small 'antigravity' force that is overwhelmed by normal gravitaiton at normal ranges but only becomes dominant at the largest scales when the average density, and hence normal gravitational forces, are small enough.

Right, but what about this matter of scale? Are you saying that DE which can push whole, gazillion-ton-mass galaxies around at a separation distance of milions of light years can't push a couple of virtually massless particles around at a distance of a 100,000 light years? Why?

 

[Garth]

Right, but what about this matter of scale? Are you saying that DE which can push whole, gazillion-ton-mass galaxies around at a separation distance of milions of light years can't push a couple of virtually massless particles around at a distance of a 100,000 light years? Why?

Basic Newton: The gravitational force acting on a body is proportional to its mass, therefore it can "push" "gazillion-ton-mass galaxies" as easy as "a couple of virtually massless particles". Cannon balls and feathers fall at the same rate in vacuo.

In GR the Equivalence Principle says the same thing: "gazillion-ton-mass galaxies" and "virtually massless particles" all 'travel' along their geodesics of curved space-time (although this is a simplification for an extended mass such as a galaxy).

DE modifies that space-time either because of the presence of a cosmological constant, or the presence of some exotic 'quintessence' with density & pressure that meets the DE equation of state. It is, however, negligible except at the largest (galactic cluster) scales where the average density drops to within a few OOM of the DE energy-density.

I hope this helps.

Garth

 

[ubavontuba]

Round and round we go...

Basic Newton: The gravitational force acting on a body is proportional to its mass, therefore it can "push" "gazillion-ton-mass galaxies" as easy as "a couple of virtually massless particles".

Sure, but this would mean the DE would have to be acting in concert on the whole universe, rather than arising out of individual low density areas (that is it couldn't be "vacuum energy"). This is because the acceleration from galaxy to galaxy must be relatively identical, or mass would tend to be pushed together by larger voids into smaller voids and small, "Big Crunches" would be the result. Also, since it has been noted that DE appears to be elongating certain mass accumulations (preventing star formation), we can tentatively say it has direction, or a vector/vectors. In other words, it must be a directional (radial?) pulling force/expansion and not a pushing force from between mass concentrations. Essentially, this leads into my question in the thread "Are we in a black hole?"

Cannon balls and feathers fall at the same rate in vacuo.

This isn't entirely true. This only happens in the gravitational field of overwhelmingly large mass as opposed to the two dropped objects. For instance, two cannon balls 1mm apart in space will fall nearly twice as fast together as a cannonball and a feather will.

In GR the Equivalence Principle says the same thing: "gazillion-ton-mass galaxies" and "virtually massless particles" all 'travel' along their geodesics of curved space-time (although this is a simplification for an extended mass such as a galaxy).

Actually, since the gazillion-ton-mass mass of a galaxy creates its own space-time geodesic, it will not fall nor accelerate the same as a particle point mass in DE (if DE behaves like an 'antigravity' force). In fact, the point masses should shoot out way ahead of galaxies from similar starting points under the influence of this hypothetical version of DE, as they will essentially not be attracted to one another by gravity like galaxies would (that is, if DE was a pushing force originating from voids, rather than an expansion force acting on the universe as a whole).

DE modifies that space-time either because of the presence of a cosmological constant, or the presence of some exotic 'quintessence' with density & pressure that meets the DE equation of state. It is, however, negligible except at the largest (galactic cluster) scales where the average density drops to within a few OOM of the DE energy-density.

As I said above, it must then act on the whole universe at once and not be localized in any way, or local crunches would result.

Therefore, instead of looking for a mysterious "dark energy" acting between the galaxies, wouldn't Occam's razor tell us to look instead to a universal gravitational attraction to the cosmological event horizon (CEH) by all mass in the universe? That is, wouldn't the act of everything falling toward the CEH explain all of the observed phenomena associated with DE?

Or, isn't it easier to say the universe is accelerating toward the CEH as if it was falling outward, rather than confusing the issue by invoking a new force to explain it?

See? Dark matter, conservation, and gravity (local and universal) make sense to me. Dark matter, gravity and a separate "dark energy force" just doesn't seem to work so well.

I hope this helps.

It helps to explain the current thinking, but it still doesn't do much to my original questions regarding the validity of two entities, dark matter and dark energy, working together in one universe.

Does this sound like a reasonable approach?

 

[Garth]

. For instance, two cannon balls 1mm apart in space will fall nearly twice as fast together as a cannonball and a feather will.

You need to think about that one, ever heard of Galileo?

Garth

 

[ubavontuba]

two cannon balls 1mm apart in space will fall nearly twice as fast together as a cannonball and a feather will.

You need to think about that one, ever heard of Galileo?

Sure. The cannon balls each fall .5mm. The feather falls nearly a full 1mm. If the acceleration is the same, the shorter distance is quicker, right?

 

[SpaceTiger]

Aren't you essentially saying the facts fit the model without examining the facts?

"Examining the facts" requires one to run large simulations -- the model we explored is only good for understanding the concept. As we've been telling you repeatedly, these simulations have been done and the results are as we're saying.

If there is this fine line in regards to galaxy cluster formation that essentially creates a demarcation line between gravity and DE, why do galaxy clusters come in so many different sizes and densities?

Nothing we've discussed prevents the formation of galaxy clusters over a large dynamic range in size and density. The more overdense a cluster is, the larger it can be before dark energy shows its effects.

I feel I understand your DE orbital model, but have problems with it in accordance with dark matter (DM). As DE pushes orbits apart, angular momentum decreases faster than gravity decreases, therefore stability is achieved (albeit in a slightly higher orbit).

No, angular momentum is conserved. That, along with energy conservation, is what prevents the orbit from being "pushed" too far.

Modelling this on a large scale, it would seem that DE would tend to make orbits higher and slower. However, we observe galactic orbits to be too low and fast due to DM.

The observations of "fast" orbits due to DM are typically on scales that are too small for DE to have a noticable influence.

The only way I see this working is if DM doesn't react with DE at all, but only with gravity. But like I said earlier, logic rules this out since it is obvious that DE reacts with gravitational mass and DM is purportedly a gravitational mass, therefore DE should react with DM. (I forget the name of this logic form).

The theory does not have the DE and DM directly interacting, only indirectly by their gravitational influence. For practical purposes, DM leads to attractive gravity, DE to repulsive gravity.

See? It's not dark matter or dark energy individually as hypothesis that I have a problem with. It's that when you combine them in accordance with NM, they tend to look rather messy. Has anyone else noticed this?

DM and DE do interact gravitationally, of course, but there are no paradoxes or "radiating galaxies". It is exactly as you have been told and it seems clear that your misunderstanding of Newtonian Mechanics is holding you back here, so I suggest we make sure you understand that before proceeding any further.

 

[SpaceTiger]

Sure, but this would mean the DE would have to be acting in concert on the whole universe, rather than arising out of individual low density areas (that is it couldn't be "vacuum energy").

You're overinterpreting "vacuum energy". In standard theory, DE does exist everywhere.

Actually, since the gazillion-ton-mass mass of a galaxy creates its own space-time geodesic, it will not fall nor accelerate the same as a particle point mass in DE (if DE behaves like an 'antigravity' force). In fact, the point masses should shoot out way ahead of galaxies from similar starting points under the influence of this hypothetical version of DE, as they will essentially not be attracted to one another by gravity like galaxies would (that is, if DE was a pushing force originating from voids, rather than an expansion force acting on the universe as a whole).

You're giving the appearance of a person trying to lift the Chrysler building with their bare hands. If you want to understand cosmology at this level, you should start simple and gradually build the machinery necessary to tackle advanced problems. It's not a good use of time for either one of us to try to unravel your misunderstandings at the advanced level when they're based on a flawed intuition (and lack of quantitative skill) in basic physics.

 

[ubavontuba]

Aren't you essentially saying the facts fit the model without examining the facts?

"Examining the facts" requires one to run large simulations -- the model we explored is only good for understanding the concept. As we've been telling you repeatedly, these simulations have been done and the results are as we're saying.

Right, but I'm questioning whether DE and DM have been properly applied in these models together? That is, have the rammifications of their interactions been considered? So far you've asserted that models have been run, but not that the potential interactions between these two forces has been run.

Nothing we've discussed prevents the formation of galaxy clusters over a large dynamic range in size and density. The more overdense a cluster is, the larger it can be before dark energy shows its effects.

Sure, but what about large but relatively thin clusters? How do they maintain their size under the same conditions?

No, angular momentum is conserved. That, along with energy conservation, is what prevents the orbit from being "pushed" too far.

Okay then, I didn't attend a class on orbital dynamics. So what you are saying is that higher orbits must normally have a higher corresponding angular momentum, right? So, what I really mean is that the requirement for the angular momentum at a particular distance is increased, not that the actual angular momentum decreases.

Since the angular momentum is not increased with the application of DE, a balance is struck where DE butresses the height of the orbit for an orbit where the angular momentum would normally be insufficient to maintain it. Is that better?

The observations of "fast" orbits due to DM are typically on scales that are too small for DE to have a noticable influence.

Yes. I will agree with this in principle. I'm only contending that under Newtonian considerations DE should nibble away at the edges of this effect. It might be a slow process (undectable?) or not. But, under simple Newtonian conditions these two supposed forces contradict each other, possibly in ways that haven't been properly modeled.

The theory does not have the DE and DM directly interacting, only indirectly by their gravitational influence. For practical purposes, DM leads to attractive gravity, DE to repulsive gravity.

Sure, that's how it's modeled. My question is; is this model correct? Simply put, if you add a quantity (gravity) and counter it with a negative quantity (antigravity) then you are simply left with less gravity, not two distinct entities.

DM and DE do interact gravitationally, of course, but there are no paradoxes or "radiating galaxies". It is exactly as you have been told and it seems clear that your misunderstanding of Newtonian Mechanics is holding you back here, so I suggest we make sure you understand that before proceeding any further.

Are you proposing a test?

You're overinterpreting "vacuum energy". In standard theory, DE does exist everywhere.

Right. Isn't that what I said? I'm simply stating that it cannot be density dependent (locally) since it must act on the whole universe in concert. Perhaps it is density dependent in regards to the whole universe, but must this be so? Is there no other possible considerations?

You're giving the appearance of a person trying to lift the Chrysler building with their bare hands. If you want to understand cosmology at this level, you should start simple and gradually build the machinery necessary to tackle advanced problems. It's not a good use of time for either one of us to try to unravel your misunderstandings at the advanced level when they're based on a flawed intuition (and lack of quantitative skill) in basic physics.

Well, now you've gone and outright insulted me. Is this the best discourse you can provide?

I'm merely posing questions. Questions that may or may not be important. All I'm asking for is answers. If you don't want to provide answers, that's okay with me. You needn't be rude.

 

[SpaceTiger]

Right, but I'm questioning whether DE and DM have been properly applied in these models together? That is, have the rammifications of their interactions been considered? So far you've asserted that models have been run, but not that the potential interactions between these two forces has been run.

No, in fact, that's exactly what I'm saying. Their gravitational interaction is considered in simulations, just as we considered it in the toy model.

Sure, but what about large but relatively thin clusters? How do they maintain their size under the same conditions?

Cluster density profiles are usually pretty similar from one to the next. I'm not aware of any that are too "thin" to be held together in the presence of dark energy.

Okay then, I didn't attend a class on orbital dynamics. So what you are saying is that higher orbits must normally have a higher corresponding angular momentum, right? So, what I really mean is that the requirement for the angualr momentum at a particular distance is increased, not that the actual angular momentum decreases. Is that better?

Yes.

Yes. I will agree with this in principle. I'm only contending that under Newtonian considerations DE should nibble away at the edges of this effect. It might be a slow process (undectable?) or not. But, under simple Newtonian conditions these two supposed forces contradict each other, possibly in ways that haven't been properly modeled.

No, in a universe with a cosmological constant, this is not true, as I've already demonstrated.

Sure, that's how it's modeled. My question is; is this model correct? Simply put, if you add a quantity (gravity) and counter it with a negative (antigravity) then you are simply left with less gravity, not two distinct entities.

Whether or not they are distinct entities or just illusions created by an alternative gravity model is something that is yet to be determined. The properties of the DM and DE, as well as the theoretical guesses as to their identities, suggest that they are in fact distinct entities.

However, there is nothing inherently wrong with the DM+DE theory, at least nothing like what you're suggesting.

Are you proposing a test?

I'm proposing that you start your questions at a more basic level. I will elaborate via PM and please refrain from posting here until we've talked things out privately.