Questioning the cosmological principle

[tom.stoer]

The cosmological principle essentially says that there are no preferred locations and directions in the universe (homogenity and isotropy). We know that strictly speaking this principle is violated at the accessible scales (filaments, galaxy clusters and supercluster, voids, CMB). So one could try to save this principle by assuming that beyond the accessible scales these inhomogenities will be smoothed out.

I think that one could equally well assume that instead the (infinite) universe has a kind of "fractal structure" extending on all scales. That would mean that the universe is filled by scale-free clusters, superclusters, ... and voids, super-voids etc.

Is this reasonable? And - if true - could it affect standard cosmology?

 

[marcus]

...
Is this reasonable? And - if true - could it affect standard cosmology?

I can't say if or how it would affect standard cosmology. Maybe someone else can respond to that. FWIW (for whatever it's worth) it seems reasonable to me that you'd have some random irregularity upwards at all scales.

So all we can know or estimate is the effective density over the largest scale we can observe and then we assume that whatever is out beyond that is either too far away to have an effect or enough like what we see that we can get good answers by assuming uniformity.

In other words, cosmologists seem to me to show an occupational trait of pragmatic ruthlessness. The cosmological uniformity principle so far seems to work and the universe conforms pretty much to the equations and we get numbers, so what the hell.

On the other hand, there is the famous case of David Wiltshire, of Uni-Canterbury, Christchurch New Zealand.

He has written a number of papers saying you don't need the Cosmo Constant to explain accelerated acceleration. You don't need the imagined "dark energy" because (he argues) we are in the middle of a kind of void with much denser universe out beyond our horizon which is pulling on stuff and making it accelerate away. To me personally this is anathema. But this may mere blind obstinacy on my part.

A personal not very considered view.
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[tom.stoer]

thanks marcus; I know the papers regarding the cc explained via a huge void; that was one reason for me to think about it

 

[marcus]

I thought you might know of David Wiltshire's papers :-D

I know he's highly regarded by a lot of people. I know I'm biased and also poorly qualified to judge. It looks to me as if Wiltshire's idea has lost steam since about 2007. I'd like to say it did not catch on. A kind of "judgment of history" except we know history can change her mind.

My bias is in favor of there simply just being this cosmological constant Lambda. It seems natural for the equation to have that constant, no reason there shouldn't be. It's not a problem for me. It seems to me that Wiltshire is the one who is making complications trying to get rid of Lambda. i think he goes against the advice of Okham (to keep it simple.)

And, in a way, the cosmo uniformity principle that you mentioned is also Okham. The simplest thing to assume where we can't see is sameness (as long as that seems to work and give OK numbers). To assume anything else besides sameness you have to make up stuff.

======================

To get clear of personal bias, I know that people have written papers on what the arguments and evidence for the cosmological principle are. It constantly gets re-considered. I see these papers and forget their names. George Jones might know some recent papers that review the status of the Principle.

 

[Tanelorn]

Nevertheless it is interesting to see all possible explanations for an effect no matter how unlikely. Especially an effect that needs something mysterious like dark energy, which is not understood. Brainstorming all possible explanations can be helpful.

 

[6nqpnw]

In spirit of your 'fractal scale' reference, there are some recent studies that somewhat support this. This is just an entertaining thought experiment, so here goes.

Whether or not she's on the forefront of these studies, Janna Levin keeps popping up on most studies / papers I'm finding in regards to black hole orbits. She has shown with computer models how a smaller black hole orbiting a much larger black hole follows a cloverleaf pattern. This same pattern is found elsewhere in nature: atoms. So in a sense, the smaller BH becomes the equivalent of an electron; and the larger a proton. She also shows how adding black holes creates 'fundamental orbits' that mirror the Periodic Table of Elements.

Scaling up to clusters, super-clusters and voids, etc. reveals a pattern similar to organic tissue. From here we can get really outragous and speculate that galaxies could be the equivalent of blood cells in an organism we call the universe.

Dunno how the CMB or CosmoConst would fit into this, but maybe it'd make for a good ending in "Men in Black III"

- mudbug | 6nqpnw -

"Imagination is Everything." - Einstein
"To know nothing is to know everything." - Confucius

 

[Chalnoth]

Well, what we can be sure of is that at very large scales, where linear behavior dominates, large scale structure most certainly is not fractally-distributed. To have a system approach a fractal distribution, you need, at the very least, to have some non-linear dynamics at work. The basic reasoning here is that in chaos theory, a chaotic system is one in which there are attractors which are fractals. But a linear system simply doesn't have any attractors at all.

In fact, Hamiltonian systems don't have attractors, so there may be some reason to believe that it may be impossible for chaos theory to have anything to say about large scale structure. However, that said, I suppose it may be possible that the dissipation of energy that galaxy clusters and smaller go through just might break this enough to allow for chaos theory to have something to say. Here's where my knowledge of the subject becomes very limited, but at the very least the fact that galaxies tend to relax into one of two very specific configurations makes it at least somewhat reasonable that galaxy dynamics can be understood in the context of chaos theory with two fractal attractors (elliptical and spiral). As far as I know, nobody has successfully applied chaos theory to structure formation, but I wouldn't rule it out as being impossible just yet.

 

[tom.stoer]

Well, what we can be sure of is that at very large scales, where linear behavior dominates, large scale structure most certainly is not fractally-distributed. To have a system approach a fractal distribution, you need, at the very least, to have some non-linear dynamics at work. The basic reasoning here is that in chaos theory, a chaotic system is one in which there are attractors which are fractals. But a linear system simply doesn't have any attractors at all.

There's one idea which may support the scale-free structure. First of all I think "fractal-like" is confusing as one might think that one can zoom in; of course this is not true; it's not about zooming in but zooming out.

Think about a thermodynamical system like boiling water at the critical point. We now from the theory of phase transitions that the fluctuatios of such as system become scale free. The steam bubbles in water can become arbitrary large (provided that there is no boundary of the system). Suppose there was such a phase transition in the universe and that the fluctuations we see today have something to do with a structure formation near the phase transition. Then it seems reasonable that the structures we see today are nothing else but these magnified, scale free bubbles.

Of course after the phase transition local interactions will change these structures. But this does not work on arbitrary large scales as there is no interaction (or at least no interaction which is strong enough; e.g. galaxy formation happens at much smaller scales). So my idea is that on larger scales these structures may have survived. And remember: in an open universe the length scale is not bounded from above, the length scale can become arbitrary large!

I think this should explain why I need neither a non-linear interaction, nor a fractal attractor in the usual sense. The phase transition will do the job.

 

[Chalnoth]

Well, we do get a nearly scale-invariant primordial structure due to inflation, but gravity acts very differently at different scales leading to significant differences later on.

 

[tom.stoer]

Well, we do get a nearly scale-invariant primordial structure due to inflation, but gravity acts very differently at different scales leading to significant differences later on.

Gravity can't act on scales larger than the cosmological horizon.

 

[Jorrie]

Gravity can't act on scales larger than the cosmological horizon.

Granted, but question: could effects of pre-inflation gravitational interactions between inhomogeneous regions outside of the present cosmological horizon still be observable today?

If so, would such effects have been largely (but not completely) 'smoothed-out' by inflation, just like other inhomogeneities?

-J

 

[Chalnoth]

Granted, but question: could effects of pre-inflation gravitational interactions between inhomogeneous regions outside of the present cosmological horizon still be observable today?

If so, would such effects have been largely (but not completely) 'smoothed-out' by inflation, just like other inhomogeneities?

-J

For the most part, it is impossible for anything that occurred before a certain time to have any effect on our current universe. The basic argument here is that due to the exponentially-accelerated expansion of the universe, it would require information to travel faster than light for these things to have any impact.

There is to date only one exception I've seen, and that is asymmetric inflation: if inflation expands very slightly differently in one direction compared to the others, then some limited amount of information from the previous state occurs. But we would be able to see this effect in the CMB, and so far it is not apparent.

 

[Jorrie]

There is to date only one exception I've seen, and that is asymmetric inflation: if inflation expands very slightly differently in one direction compared to the others, then some limited amount of information from the previous state occurs.

Isn't the possible "http://www.nasa.gov/centers/goddard/news/topstory/2008/dark_flow.html" " another exception, or is it the same thing?

I was thinking along these lines: if two regions were put into relative motion by inhomogeneous gravitation before inflation happened, then may some of that relative motion not be remaining today, despite now being outside of each others particle horizons?

-J

 

[Chalnoth]

Isn't the possible "http://www.nasa.gov/centers/goddard/news/topstory/2008/dark_flow.html" " another exception, or is it the same thing?

This is a different issue, but I am highly, highly skeptical of this result. We'll see what Planck has to say about it. But I'd have to learn more about the Grischuk-Zeldovich effect to say more on what this has to say about super-horizon configurations.

I was thinking along these lines: if two regions were put into relative motion by inhomogeneous gravitation before inflation happened, then may some of that relative motion not be remaining today, despite now being outside of each others particle horizons?

The point is that all of the observable universe today stemmed from inflation. Anything that was going on before inflation occurred has been expanded to be so much larger than the current observable universe as to be completely unimportant for any of our observations.

 

[Jorrie]

The point is that all of the observable universe today stemmed from inflation. Anything that was going on before inflation occurred has been expanded to be so much larger than the current observable universe as to be completely unimportant for any of our observations.

Understood. Thanks :)

 

[inflector]

Gravity can't act on scales larger than the cosmological horizon.

Can you please elaborate on the reasons for this? I could see how it can't act currently, but could it not have been acting since the Big Bang and therefore have an effect on what is currently within the horizon?

Couldn't structure at the horizon + 100 LightYears have affected the relationship between the structure just within the horizon and the structure closer to us due to an interaction that occurred shortly after the Big Bang?

EM radiation has limits imposed because of the opacity of matter until the time of last scattering at around 380,000 years but gravity has no such limit right? So isn't all the matter in the universe potentially causally connected by gravity?

 

[Chalnoth]

Can you please elaborate on the reasons for this? I could see how it can't act currently, but could it not have been acting since the Big Bang and therefore have an effect on what is currently within the horizon?

Couldn't structure at the horizon + 100 LightYears have affected the relationship between the structure just within the horizon and the structure closer to us due to an interaction that occurred shortly after the Big Bang?

EM radiation has limits imposed because of the opacity of matter until the time of last scattering at around 380,000 years but gravity has no such limit right? So isn't all the matter in the universe potentially causally connected by gravity?

From what I recall, the effects of whatever may exist beyond our cosmological horizon artfully cancel out within it. If you think about it, something like this must occur, or else we could obtain information about things which have always been causally disconnected from us.

 

[inflector]

From what I recall, the effects of whatever may exist beyond our cosmological horizon artfully cancel out within it. If you think about it, something like this must occur, or else we could obtain information about things which have always been causally disconnected from us.

I'm not proposing that we could obtain information about things which have always been causally disconnected from us.

I'm proposing the idea that we can't really say what has been causally disconnected from us since gravity also creates a causal connection and therefore any portion of the universe that has been within our gravitational reach at any time since the big bang might have effected us. In effect, I'm questioning the very proposition that there is any portion of the universe which we can say is causally disconnected from a gravitational perspective.

I'm interested in the idea of a cancellation, however, even if I don't yet understand why something like that must have occurred. Any references to papers, books, or suggestions for googling?

 

[Chalnoth]

I'm not proposing that we could obtain information about things which have always been causally disconnected from us.

I'm proposing the idea that we can't really say what has been causally disconnected from us since gravity also creates a causal connection and therefore any portion of the universe that has been within our gravitational reach at any time since the big bang might have effected us. In effect, I'm questioning the very proposition that there is any portion of the universe which we can say is causally disconnected from a gravitational perspective.

I'm interested in the idea of a cancellation, however, even if I don't yet understand why something like that must have occurred. Any references to papers, books, or suggestions for googling?

Well, the basic idea is that the effects of whatever happens outside the cosmological horizon maps onto the boundary conditions at the horizon. Here's one paper that goes into detail about the issue, in the context of attempting to use super-horizon perturbations to explain the accelerated expansion:
http://arxiv.org/abs/gr-qc/0702043

They claim the effect is "real", but I have no idea what this means when they also demonstrate that the entirety of the effect can be represented as surface terms.

 

[TrickyDicky]

The cosmological principle essentially says that there are no preferred locations and directions in the universe (homogenity and isotropy). We know that strictly speaking this principle is violated at the accessible scales (filaments, galaxy clusters and supercluster, voids, CMB). So one could try to save this principle by assuming that beyond the accessible scales these inhomogenities will be smoothed out.

I think that one could equally well assume that instead the (infinite) universe has a kind of "fractal structure" extending on all scales. That would mean that the universe is filled by scale-free clusters, superclusters, ... and voids, super-voids etc.

Is this reasonable? And - if true - could it affect standard cosmology?

You bet it could, it would be back to the drawing board for cosmology, in the words of cosmologist David Hogg. There is a quite interesting debate about this going on for the last 4-5 years, and the good thing is if the galctic redshift surveys keep cumulating data at the current pace in a few years we'll have enough info to solve the debate one way or the other.
At this point all we can say is that the fractal inhomogeneity could actually smooth out at some point beyond 100 Mpc or else the fractal structure could go on and we might find "hyperclusters": groupings of superclusters. If we do gather observational info from the galactic surveys that show this kind of structures to say that it will affect the standard cosmology is a huge understatement, it's more like standard cosmology would be death and buried, and as Hogg says in the link it's back to the board.
On the other hand if from the data from redshift surveys we find homogeneity with a big enough sample of galaxies and no such hyperclusters and hypervoids type of structures, standard cosmology gets yet another confirmation.

For those interested in this exciting debate:
http://magickriver.blogspot.com/2007/10/is-universe-fractal-by-amanda-gefter.html

 

[tom.stoer]

I not quite sure if I understand correctly.

First of all it's clear that if we find indications of such "fractal-like" structures within the observable universe it will be a challange for cosmology, but I can't see why this would really mean "back to the drawing board". Which principle or currently agreed result would be violated and what would cause severe problems? (the cosmological principle is an approximation at large scales only).

If we do not find these structures within the observable universe the situation could be even more strange. We could assume both a) fractal-like structures or b) a smooth structure according to the cosmological principle on scales _beyond_ the obervable universe; but both options would not cause any observational effect and are therefore hidden from being investigated in principle.

 

[TrickyDicky]

I not quite sure if I understand correctly.

First of all it's clear that if we find indications of such "fractal-like" structures within the observable universe it will be a challange for cosmology, but I can't see why this would really mean "back to the drawing board". Which principle or currently agreed result would be violated and what would cause severe problems? (the cosmological principle is an approximation at large scales only).

Actually it's easy to understand, the FRW metric is built on the cosmologic principle in its strong form, the one that assumes that isotropy implies spatial homogeneity of the universe at large scale. But there is a weaker form of the cosmological principle called "conditional cosmologic principle" stated by Mandelbrot in 1982, that says that in a fractal universe isotropy doesn't imply spatial homogeneity, instead it would be compatible with spatial inhomogeneities at large scale(hyperclusters, hyper-hyperclusters...) and would still retain "statistical homogeneity" for a sufficiently large spacetime scales.
But this is forbidden for a cosmology based on the FRW metric, as there would be no congruence of observers to see an increase of density with time,there would be no scale factor and no Hubble flow without spatial homogeneity there is no spacelike hypersurfaces of constant density sliced by the FRW metric and there is no positive mean density, and therefore no FRW metric is possible in a fractal universe, and without it the interpretation of cosmological redshift as expansion is not possible either.
So if you read the link you'll understand why mainstream cosmologist David Hogg says there is no way our universe could be fractal with our current paradigm, and if it turns out to be so, then we have to come up with a new model and forget about Big Bangs, expansion and all the lot.
Actually the discovery of superclusters already strained a bit the model, and we are relying on dark matter distributions that haven't been confirmed, if we consistently found out structures bigger than that with the galactic redshift surveys( the first of such structures has already been found in 2003 it is called the Sloan Great Wall and is classified as hypercluster SCl 126) it would be time to change the model.

 

[Chalnoth]

I'm a bit suspicious of this claim. It is definitely true, after all, that our universe is not actually FRW. It has inhomogeneities.

This is why the perturbed FRW framework was constructed. In principle, perturbed FRW, expanded to sufficient accuracy, should be able to describe any cosmology (provided General Relativity is accurate). In practice, the linear solutions to a perturbed FRW metric describe our universe to very good accuracy at larger scales, so I don't think there's really any question that this picture works.

The only question is whether or not we should start routinely adding correction terms to the overall expansion rate due to the inhomogeneities.

 

[TrickyDicky]

It is definitely true, after all, that our universe is not actually FRW. It has inhomogeneities.

This is why the perturbed FRW framework was constructed. In principle, perturbed FRW, expanded to sufficient accuracy, should be able to describe any cosmology (provided General Relativity is accurate). In practice, the linear solutions to a perturbed FRW metric describe our universe to very good accuracy at larger scales, so I don't think there's really any question that this picture works.

The only question is whether or not we should start routinely adding correction terms to the overall expansion rate due to the inhomogeneities.

You are correct, sir.
The problem is if you add enough corrections, that is, if you make a strongly perturbed FRW model, you end up with statistical homogeneity as defined in a fractal universe, and then the FRW model loses all its meaning, it no longer serves to justify the Hubble flow.
So you need to put some constrain, in this article this issue is discussed with more eloquence than I can provide.

http://adsabs.harvard.edu/full/1987MNRAS.226..373S

 

[Chalnoth]

The problem is if you add enough corrections, that is, if you make a strongly perturbed FRW model, you end up with statistical homogeneity as defined in a fractal universe, and then the FRW model loses all its meaning, it no longer serves to justify the Hubble flow.

Well, yes, but we know that's not the case due to the current successes of the FRW model. Because of the successes (so far) of this model, it is absolutely clear that if there are deviations, those deviations are small.

Now, it may well be the case that a more accurate model will at the same time offer a simpler mathematical description of the expansion, but somehow I doubt it. I'd be willing to bet that if it becomes necessary to correct FRW on large scales, the most common thing to do will be to add correction terms, as that's likely to be much simpler.

 

[tom.stoer]

again, let me ask if and how a fractal structure far beyond the observational universe does affect the predictions of an FRW-based model?

 

[Tanelorn]

I wonder can this explain dark energy? As the cosmological horizon gets smaller so does the amount of gravitational force holding the observable universe together, so we get more expansion and so on and so forth.

 

[Chalnoth]

I wonder can this explain dark energy? As the cosmological horizon gets smaller so does the amount of gravitational force holding the observable universe together, so we get more expansion and so on and so forth.

Huh? The cosmological horizon is a function of the makeup of the universe. And for a universe with matter in it, the cosmological horizon tends to grow with time. You have to have very unphysical sorts of stuff for the cosmological horizon to shrink.

 

[Tanelorn]

Chalnoth thanks for reply. For some reason I had interpreted that the cosmological horizon is the observable universe horizon limit, which is shrinking because of dark energy expansion of the universe. So what is the cosmological horizon then?

Also am I correct in saying that as space expands the graviational force holding superclusters together also falls resulting in further expansion?

I presume that the speed of gravitational attraction between two galaxies moving apart at high speed is also the speed of light?

 

[tom.stoer]

I wonder can this explain dark energy?

Possibly yes!

There are research programs trying to explain the accelerated expansion (and therefore the cosmological constant) as a kind of optical illusion. For that to be true the Earth should be located near the center of a huge void.

I have to find the relevant links to the articles on arxiv.