I How is dark matter thought to have formed a network scaffolding?

[hkyriazi]

TL;DR Summary

How is dark matter, responding to gravity, thought to have formed filaments and walls--the scaffolding for the large scale structure of the universe--rather than random clumps?

The summary pretty much says it all: How is dark matter, responding to gravity, thought to have formed filaments and walls--the scaffolding for the large scale structure of the universe--rather than random clumps? I can understand how scattered matter might not coalesce while exchanging photons (and receiving momentum away from other, reflective, matter), and that dark matter, by not interacting with light after the Big Bang, might be able to form a scaffolding with sufficient mass to have matter be attracted to it, despite the photon bath. But why filaments and walls, rather than randomly, though perhaps fairly regularly, arranged clumps?

 

[kimbyd]

It's the natural result of gravitational collapse from gaussian primordial perturbations. Here's an example of one simulation which demonstrates this visually:

 

[kimbyd]

Actually, this simulation is better for the purposes of this thread:

 

[hkyriazi]

Thanks. Beautiful simulations--especially the 2nd one. In both simulations, however, it seems filamentous structures arise almost immediately. Is this because they've been placed into the models? In other words, the initial distribution of dark matter (or matter) seems decidedly non-uniform. (I don't understand what you mean by "primordial perturbations," unless you mean perturbations away from perfect homogeneity, and maybe even away from random clumpiness.)

 

[kimbyd]

Thanks. Beautiful simulations--especially the 2nd one. In both simulations, however, it seems filamentous structures arise almost immediately. Is this because they've been placed into the models? In other words, the initial distribution of dark matter (or matter) seems decidedly non-uniform. (I don't understand what you mean by "primordial perturbations," unless you mean perturbations away from perfect homogeneity, and maybe even away from random clumpiness.)

Nope! They just use uncorrelated Gaussian random perturbations as the initial state. At least, they're uncorrelated at the start. Later on they become correlated due to gravitational interactions. That's what gives rise to the filamentary structure.

 

[hkyriazi]

Can anyone explain this to me in gravitational, mechanistic terms? It's inevitable that, with a random initial distribution, there will be some units of mass closer to one another than others, and that those initially close units will coalesce in a linear arrangement (if only 2 units participate). But why is it that neighboring (dark) matter is subsequently pulled into filamentous alignments, along the axes of the 2-unit coalescences (for lack of a better term), rather than from all directions? Is it due to momentum from multi-unit approaches "pulling" the coalescences apart, like taffy, in a necessarily linear way (along the line of the net momentum of approach)? I don't recall seeing this sort of thing in the simulations.

 

[hkyriazi]

I must take that last comment back. The first simulation (but not at all the 2nd) does indeed show such motions within the coalescences, and a lengthening effect of momentum--especially at the very end.

 

[hkyriazi]

They just use uncorrelated Gaussian random perturbations as the initial state. ... Later on they become correlated due to gravitational interactions. That's what gives rise to the filamentary structure.

Is my understanding of exactly how those filaments arise reasonable/correct in your view? (See previous two responses--though subsequent to your quoted comments.)

 

[KurtLudwig]

Still it is hard to imagine how these huge voids and walls formed. The software could have been written with a bias towards making these structures form. Could the voids and walls have been caused by catastrophic explosions of massive stars early in structure formation? (My suggestion is probably nonsense.)

 

[Vanadium 50]

The software could have been written with a bias towards making these structures form

Sure. You can always dismiss work as the product of liars and knaves. But then no evidence whatsoever will convince you.

My suggestion is probably nonsense.

I agree.

 

[hkyriazi]

Still it is hard to imagine how these huge voids and walls formed. The software could have been written with a bias towards making these structures form. ...

It may relate to the simulations adding spatial expansion, and the way they decided to implement it. (The 1st video explicitly states this in the YouTube caption, which is why matter gets more and more sparse as it progresses. Not the case in the 2nd video, at least in terms of its visual presentation.) My understanding is that there's some scale below which expansion is thought NOT to occur. For example, our own atoms are not considered to be getting bigger. One assumes the same is true on the solar system scale. If they extend that exclusion to galaxy clusters of a certain size, one would necessarily get void spaces.

I'm still not sure about the walls, though. My idea about gravitational attraction causing momentum in the coalescing group to get pulled into filaments, like taffy, doesn't seem to be able to account for walls.

 

[KurtLudwig]

I did not mean to imply that some physicists are dishonest. But every person wants to defend his favorite hypothesis or theory and may sometimes tend to interpret data toward a desired outcome. Statistical analysis is sometime tricky. I was thinking more about efficacy of drugs and vaccines. I do apologize if I gave that impression.

 

[Vanadium 50]

So instead of knaves and liars, they are just fools?

Do you have any specific objection? Or is it simply that their work is inconsistent with your own theory?

 

[PeterDonis]

I was thinking more about efficacy of drugs and vaccines.

Which has nothing to do with numerical simulations using physical laws.

Vague suggestions of "bias" are not helpful.

 

[KurtLudwig]

Certainly, I do not think that they are fools or malevolent. I joined physics forums to learn from you. If I made an unfortunate statement, I am sorry. At this time, I am not knowledgeable enough in physics to make an informed judgement. What I meant was that during biological testing of drugs and vaccines, double-blind studies are needed to eliminate a researcher's "unconscious" bias. However, I would rather redirect the conversation towards how these huge voids and walls formed in our Universe. So the best method is to make geometrical models.
(Since I have joined physics forums, I have read half a dozen "entertainment" physics books, such as the "Hidden Reality" by Brian Greene and "The First Three Minutes" by Steven Weinberg. At your or your colleagues suggestions, I am now reading physics textbooks, with the related mathematics. I have finished reading "An Introduction to Modern Cosmology" by Andrew Liddle. Currently, I am reading, and am struggling with the mathematics, in "An Introduction to General Relativity and Cosmology" by Christian Boehmer. It is humbling to realize the mathematical formulae and geometric models of space-time which modern physicists have created.)
Since you requested a specific example of a perceived bias in the physics community: It is Dark Matter vs. MOND. I maybe biased in partially supporting MOND. Still, I believe that MOND is simpler and more convincing in explaining the rotation curves of stars in our galaxy. MOND is tightly constrained by the value of their constant a0, whereas dark matter's location is just given by a halo. So dark matter is distributed to uphold Newton's Law of Universal Gravitation in very weak gravitational fields. This looks like a bias to me. arXiv:astro-ph/02044521v1 Modified Newtonian Dynamics as an Alternative to Dark Matter. There was an article in Scientific American asking the physics community to stop ignoring MOND.
Without a doubt, dark matter was needed in the formation of the structure of the early universe. It may not be elegant that the existence of dark matter and MOND may be needed to explain the structure of our universe and its dynamics, but then in 1937 the mu meson was discovered which was unexpected and upset the then standard model of particles. (I was taught about its discovery in college during the 1960s.)
Again, I defer to the judgement of the physics community.

 

[Vanadium 50]

There is a certain class of individual who comes here with their own theories (e.g. "the voids and walls have been caused by catastrophic explosions of massive stars early in structure formation) and are dismissive of actual scientists (bias). Such people are not taken seriously, as well they shouldn't. Your decision is whether you want to keep posting like them and risk getting lumped in with them or not.

Reading a book by Brian Greene does not make one a theorist. In the case in question, the smallest elements of large-scale structure contain 1,000,000,000,000,000,000's of stars. I write it longhand so you can see that a few stars exploding hither and yon cannot possibly cause the structure that we see. Sorry, but your theory postulates a source that is more than a dozen orders of magnitude too small.

As far as MOND as proof of bias, that's again nonsense. It's discussed in the scientific literature, and as you yourself admit, it's even in Scientific American. Most scientists do not find it a convincing theory because it works on galactic scales and nowhere else.

 

[PeterDonis]

It is Dark Matter vs. MOND. I maybe biased in partially supporting MOND. Still, I believe that MOND is simpler and more convincing in explaining the rotation curves of stars in our galaxy.

You misunderstood my statement about bias. Science is not a matter of assessing people's bias, still less a matter of trying to decide who is less biased or whose explanation you believe is more convincing, or saying that you have a hard time imagining how a particular type of model could work. Science builds models and tests them against data. So the only relevant subject for discussion here is, what are the models and how well do they match the data? Anything else is off topic.

 

[PeterDonis]

Thread has been reopened at OP's request.

 

[hkyriazi]

Does anyone have in mind a gravitational mechanism for how walls/sheets of filaments form, i.e., for why there are 2D arrangements of galaxies? (I think I have a handle on the (1D) filaments--see comment #11.)

 

[kimbyd]

Does anyone have in mind a gravitational mechanism for how walls/sheets of filaments form, i.e., for why there are 2D arrangements of galaxies? (I think I have a handle on the (1D) filaments--see comment #11.)

I don't think there's a really simple, obvious answer for this. Basically it's just a matter of gravitational collapse from random initial conditions, which is to say that you start with a nearly-uniform random field, and then gravitational collapse amplifies any structures which were there to begin with. The nature of the initial random distribution tends to favor some kinds of shapes over others once significant collapse has occurred.

 

[Ibix]

This is naive, but if we have over-dense regions that collapse and shrink, aren't we saying that the under-dense regions grow? So should we not expect large voids bounded by thin shells of matter?

 

[kimbyd]

This is naive, but if we have over-dense regions that collapse and shrink, aren't we saying that the under-dense regions grow? So should we not expect large voids bounded by thin shells of matter?

Yup, basically. So the voids can be basically visualized as bubbles, and the places where the bubbles connect become the observed filamentary structure. The number and orientation of connecting bubbles determine the shape of that structure.

Of course, this isn't exact, as there are no actual membranes involved. So this visualization shouldn't be taken too seriously.

 

[hkyriazi]

I don't think there's a really simple, obvious answer for this. Basically it's just a matter of gravitational collapse from random initial conditions, which is to say that you start with a nearly-uniform random field, and then gravitational collapse amplifies any structures which were there to begin with. The nature of the initial random distribution tends to favor some kinds of shapes over others once significant collapse has occurred.

The evolution of filaments I seem to understand, as mentioned above (comment #11), based solely on gravitation and momentum acting on a random distribution of (dark) matter. And when we add in the models' spatial expansion aspect, which kicks in only at very large separation distances, I can vaguely visualize how sheets/walls would form: filaments near and side-by-side one another would not have space added in between them, but space would be added on either side defined by their plane, thus establishing them, and others near them, into a planar arrangement. More broadly, as someone else mentioned in another comment, regions of space that happen to be empty to the extent dictated by the spatial expansion routine (i.e., "soap bubbles") would grow, in essence seeming to "push" the matter-occupied regions into planar arrangements.

I was wondering if there are any purely gravitational mechanisms for the evolution of walls. (I can't believe they'd exist in a predominant, systematic way in any truly random initial arrangement.)

 

[kimbyd]

The evolution of filaments I seem to understand, as mentioned above (comment #11), based solely on gravitation and momentum acting on a random distribution of (dark) matter. And when we add in the models' spatial expansion aspect, which kicks in only at very large separation distances, I can vaguely visualize how sheets/walls would form: filaments near and side-by-side one another would not have space added in between them, but space would be added on either side defined by their plane, thus establishing them, and others near them, into a planar arrangement. More broadly, as someone else mentioned in another comment, regions of space that happen to be empty to the extent dictated by the spatial expansion routine (i.e., "soap bubbles") would grow, in essence seeming to "push" the matter-occupied regions into planar arrangements.

I was wondering if there are any purely gravitational mechanisms for the evolution of walls. (I can't believe they'd exist in a predominant, systematic way in any truly random initial arrangement.)

One interesting wrinkle is that if you take linear gravity, gravitationally-bound structures don't change over time.

Actual General Relativity isn't linear at all. But you can take a simplification of General Relativity, where you have some average density and small differences from that average. This allows you to decompose the system into linear terms and non-linear terms. If you include only the linear equations, then the result has a lot of nice mathematical properties that make it easy to solve equations. And the result is accurate for the initial stages of structure formation, and remains accurate for very large scale behavior.

The picture that is painted is that we have a universe which was, in its early phases, far more dense. But some parts of the universe were more dense than others. As the universe expanded and the rate of expansion slowed, the expansion of the more dense systems would have slowed to the point that their expansion could be halted entirely. They form bound systems. And those bound systems, according to linear theory, don't change at all from then on.

Now, as I mentioned, linear theory isn't accurate at small scales. If it were, we couldn't have any galaxies. But it still provides a first-pass look at what is going on at big scales. It paints a picture where early-on, the structures don't so much form as become distilled out as the less-dense regions continue to expand. As the low-density regions expand while the more dense regions change very little, the structures become more and more apparent, because the density contrast between the more-dense and less-dense regions grows. So you can imagine that early-on, there wasn't much difference between the more-dense and less-dense regions at all. But as the less-dense regions expanded and the more-dense regions remained comparatively static, that density contrast really becomes striking, and it forms shapes very much like you'd expect from a bunch of touching soap bubbles.

 

[hkyriazi]

One interesting wrinkle is that if you take linear gravity, gravitationally-bound structures don't change over time.

Actual General Relativity isn't linear at all. But you can take a simplification of General Relativity, where you have some average density and small differences from that average. This allows you to decompose the system into linear terms and non-linear terms. If you include only the linear equations, then the result has a lot of nice mathematical properties that make it easy to solve equations. And the result is accurate for the initial stages of structure formation, and remains accurate for very large scale behavior.

The picture that is painted is that we have a universe which was, in its early phases, far more dense. But some parts of the universe were more dense than others. As the universe expanded and the rate of expansion slowed, the expansion of the more dense systems would have slowed to the point that their expansion could be halted entirely. They form bound systems. And those bound systems, according to linear theory, don't change at all from then on.

Now, as I mentioned, linear theory isn't accurate at small scales. If it were, we couldn't have any galaxies. But it still provides a first-pass look at what is going on at big scales. It paints a picture where early-on, the structures don't so much form as become distilled out as the less-dense regions continue to expand. As the low-density regions expand while the more dense regions change very little, the structures become more and more apparent, because the density contrast between the more-dense and less-dense regions grows. So you can imagine that early-on, there wasn't much difference between the more-dense and less-dense regions at all. But as the less-dense regions expanded and the more-dense regions remained comparatively static, that density contrast really becomes striking, and it forms shapes very much like you'd expect from a bunch of touching soap bubbles.

Your last two paragraphs sound pretty much like what I'd painted as a possible explanation for evolution of walls/sheets. I'm confused, though, about the relationship--if any--between GR's non-linearity and the assumption of spatial expansion. Are they synonymous, or completely unrelated? I can understand how Newtonian gravity, being thought to have infinite reach, would "bind" objects at any distance, so long as they're not moving apart at "escape velocity." Is this what you mean by purely linear gravity?

 

[kimbyd]

Your last two paragraphs sound pretty much like what I'd painted as a possible explanation for evolution of walls/sheets. I'm confused, though, about the relationship--if any--between GR's non-linearity and the assumption of spatial expansion. Are they synonymous, or completely unrelated? I can understand how Newtonian gravity, being thought to have infinite reach, would "bind" objects at any distance, so long as they're not moving apart at "escape velocity." Is this what you mean by purely linear gravity?

What determines linearity is this: if you sum up the fields from different sources, you get the correct result.

So, yes, Newtonian gravity is always linear. The gravitational effects in General Relativity don't simply sum in such a simple way. Both theories of gravity are infinite in extent, and General Relativity looks a lot like Newtonian gravity at large distances and away from very massive objects. But they definitely aren't the same thing.

Furthermore, additional non-linearity creeps in because gravity isn't the only force at work. Normal matter experiences friction and radiates energy using electromagnetic waves. This effect is mostly apparent at the level of galaxy clusters and smaller objects, however, and isn't likely to be a noticeable component of the filamentary structure (e.g. gas and dust content of a galaxy likely determines whether galaxies become spiral-shaped or elliptical). The filamentary structure is probably 90-95% described by the linear approximation, with some tweaks due to the inherent non-linearity of General Relativity.

 

[PeterDonis]

if you sum up the fields from different sources, you get the correct result.

To be clear, this is a description of linearity. Non-linearity is when this is not true.

 

[kimbyd]

To be clear, this is a description of linearity. Non-linearity is when this is not true.

Ah, yes. Edited.

 

[hkyriazi]

Is it fair to say, then, that the Cosmological Constant term in the equations of GR--which, IIRC, is how spatial expansion can come into play in a formal way--is one of the non-linearities of GR?

 

[kimbyd]

Is it fair to say, then, that the Cosmological Constant term in the equations of GR--which, IIRC, is how spatial expansion can come into play in a formal way--is one of the non-linearities of GR?

No, this is pretty far off. The Cosmological Constant isn't at all fundamental to spatial expansion, and it doesn't contribute any non-linearities. In fact, the CC part of the Einstein Field Equations is the one part that is fully linear.

 

[hkyriazi]

No, this is pretty far off. The Cosmological Constant isn't at all fundamental to spatial expansion, and it doesn't contribute any non-linearities. In fact, the CC part of the Einstein Field Equations is the one part that is fully linear.

Ah, right. I was confusing spatial expansion with the *acceleration* of spatial expansion attributed to dark energy. (Am I correct in thinking that the CC is directly related to that?)

 

[kimbyd]

Ah, right. I was confusing spatial expansion with the *acceleration* of spatial expansion attributed to dark energy. (Am I correct in thinking that the CC is directly related to that?)

Yes, that's correct.

Though the terminology around the accelerated expansion is confusing. The actual rate of expansion (velocity/distance) is and always has been dropping. The acceleration comes in because if the reduction in the rate of expansion is slow enough, then as objects move further away they'll recede at higher velocities.

That's what the cosmological constant does: it places a floor on the rate of expansion. In the far future, the rate of expansion will be a constant determined by the cosmological constant.

This floor on the rate of expansion does two main things:
1) It tends to make it a little bit harder for structures like galaxies and galaxy clusters to form, as the cosmological constant makes gravity repulsive at large distances. Large extent and low density make structures more vulnerable to disruption by the cosmological constant. This shapes what kinds of objects are more common in our universe.
2) At late times, by placing a floor on the rate of expansion, it causes an eternal, accelerated expansion where (eventually) objects are moving away from one another at an exponential rate.

At very early times, the cosmological constant was simply too small to have any impact at all, so it likely is utterly irrelevant when considering questions for the very early universe such as what caused the expansion in the first place.

 

[hkyriazi]

Yes, that's correct.

Though the terminology around the accelerated expansion is confusing. The actual rate of expansion (velocity/distance) is and always has been dropping. The acceleration comes in because if the reduction in the rate of expansion is slow enough, then as objects move further away they'll recede at higher velocities.

Thanks. This is news to me, and I'll give it some careful thought. It's reminiscent of when congress critters say they're decreasing spending, but actually are merely decreasing the rate of increase in spending.

 

[Bandersnatch]

I'll give it some careful thought.

It's educational to start off with some clearly unphysical models of expansion, that nonetheless provide a set of good intuitions by virtue of being simplified.
For example, consider a Milne model, which is one where the universe is expanding steadily - neither accelerating or decelerating.
This means that any given galaxy that you observe to have some recessional velocity at a given time, will retain this velocity forever (and has had it since the beginning).
But, the value of the Hubble parameter is still going down, because it tells you by what percentage of their current value do all distances grow per unit time. So, a galaxy starting off e.g. 1 billion light-years (Gly) away, and always receding at 1 Gly per 1 billion years (Gyr), will after 1 Gyr be 2 Gly away = distance measured between 0 and 1 Gyr has grown by 100%. After another billion years, it will be 3 Gly away = the distance measured between 1 and 2 Gyr has grown by 50% only, even though the galaxy keeps receding at a steady pace. After another Gyr it's 33% and so on.

If you treat the Milne model as an edge case, then it's perhaps easier to see that any model where galaxies experience deceleration of their recessional velocities will have the Hubble parameter go down even faster. Whereas if they experience acceleration, the Hubble parameter will either go down slower (if the acceleration is less than exponential), don't go down (if the acceleration is exponential) or go up (if the acceleration is faster than exponential).

 

[hkyriazi]

Kimbyd and Bandersnatch, it's difficult to reconcile a slowing expansion rate with this figure (attached), from the Hubblesite: http://hubblesite.org/image/1037/news_release/2001-09I

I do recall reading at various times that some value or other was close to zero, meaning that the expansion was slowing, but such as to asymptote, never truly stopping, but practically so (ensuring that there'll be no "Big Crunch," as gravity reverses the expansion). Those jibe with your comments, but someone may have to make this entry at Wikipedia more clear: https://en.wikipedia.org/wiki/Accelerating_expansion_of_the_universe

 

[Orodruin]

Do not confuse expansion rate with distance growth. In a universe with constant expansion rate, the distance between two comoving objects grows exponentially.

 

[hkyriazi]

Do not confuse expansion rate with distance growth. In a universe with constant expansion rate, the distance between two comoving objects grows exponentially.

I do get that if one defines the expansion rate as a percentage of current distance--calculated yearly or over some other time interval, I presume--the distance compounds like interest, and a constant expansion rate yields an exponential growth in size.

Am I correct in thinking there's a discrepancy between the above-posted figure (and its illustrated switch, about 7 billion years ago, from "Slowing expansion" to "Accelerating expansion"), and this statement (#32) by Kimbyd: "The actual rate of expansion (velocity/distance) is and always has been dropping"?

 

[Bandersnatch]

Am I correct in thinking there's a discrepancy between the above-posted figure (and its illustrated switch, about 7 billion years ago, from "Slowing expansion" to "Accelerating expansion"), and this statement (#32) by Kimbyd: "The actual rate of expansion (velocity/distance) is and always has been dropping"?

No, there's no discrepancy.
The curve of the bell is a velocity curve, since it relates distance traveled in time. The direction of its curvature shows the direction of acceleration (i.e. slowing expansion vs accelerating expansion).
The rate of expansion tells you - just as you described in the other paragraph above - by what fraction does the distance grow in unit time.
There's nothing contradictory in having the fractional growth go down over time and the velocity starting to accelerate.
I think you'll need to describe in more detail why you think there is one, before we can address it.

 

[hkyriazi]

No, there's no discrepancy.
[...]
There's nothing contradictory in having the fractional growth go down over time and the velocity starting to accelerate.
I think you'll need to describe in more detail why you think there is one, before we can address it.

OK, I'll give it a shot, though in reading over what I've written below, I'm not sure my fog has been lifted. ;-)

Am I correct in assuming that the folks who did the Type IA supernova data acquisition and analysis that has been interpreted as an accelerating expansion, and led to the hypothesizing of dark energy, thought they'd find instead that the amount of expansion per unit time has continually been decreasing (as in the lower half of that bell curve), and would eventually slow almost to zero, such that that bell curve would eventually have its two sides going essentially straight up (though not quite)? (And, would that constitute a "flat universe"?) I'm guessing that that initial, slowing expansion was thought to be due to the effect of gravity.

Also, am I correct in thinking that for the lower half of that bell curve to be accurate--i.e., the "size of the universe" was slowing its rate of increase--the rate of expansion (defined as a percentage of distance between "comoving objects" per time unit) had to be constantly decreasing, and by an amount larger than that required to counter the "compounding interest" aspect of that rate?

Finally, would it be correct to modify Kimbyd's statement from this: "The actual rate of expansion (velocity/distance) is and always has been dropping", to this: "The actual rate of expansion (velocity/distance) is and always has been dropping, but around 7 billion years ago the effect of gravity to slow the rate of expansion greatly dwindled, decreasing the decline in the rate of expansion to the point where the "compounding interest" aspect of the expansion rate took over, resulting in an increase in the growth of the universe's size per year"?

 

[Bandersnatch]

Yes, all of that looks fine.
Maybe apart from this bit:

but around 7 billion years ago the effect of gravity to slow the rate of expansion greatly dwindled

Insofar as there was nothing sudden or 'great' about it. The opposing effects of decelerating matter (and radiation) vs accelerating dark energy have been going on from the very beginning. At some point matter simply diluted enough for the (constant) accelerating effect to become dominant.

 

[Justin Hunt]

is 15 billion years really enough time for matter that was almost uniform to have formed into the structures of today? There is a lot of empty space between galaxies today and this movement initially would have been very slow at the start when the density was close to uniform. Would part of the solution be that the universe was much denser back then?

Also, was matter considered all bound at the start of the big bang? did parts of the big bang cause globs of matter to become unbound? Is there any discussion about when parts of the universe in general may have changed from bound to unbound or vice versa?