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.
======================

 

[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.

 

[Chalnoth]

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.

This view has been ruled out:
http://arxiv.org/abs/1007.3725

 

[Chalnoth]

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?

There have been some attempts to explain the accelerated expansion as a result of non-linear evolution of structure. The basic idea is that the overdense regions expand more slowly than the underdense regions, so that if you average over space, the underdense regions make up larger and larger fractions of that space with time, leading to an apparent acceleration.

However, more detailed studies of this have shown that it is, at most, too small a correction to the observed expansion rate to explain the observed acceleration without dark energy.

 

[Tanelorn]

Has anyone thought of building a complete simulation using all known physics of the standard model of the entire observable universe of galaxies, clusters, superclusters, hyper clusters and great wall etc? (probably need to include at least several imagined observable universes beyond our observable universe to ensure we don't have any discontinuity effects). Actually forget single galaxies they are probably insignificant!

I would think that something could be done along these lines even now with the supercomputers we have?

http://www.nowykurier.com/toys/gravity/gravity.html

This one doesn't quite cut it, but it is amazing how we end up with a single massive oject at the end.
I just managed to make a star, planet, moon and moon satelite (for one orbit of the satelite before coming unstable)!

 

[Chalnoth]

Has anyone thought of building a complete simulation using all known physics of the standard model of the entire observable universe of galaxies, clusters, superclusters, hyper clusters and great wall etc? (probably need to include at least several imagined observable universes beyond our observable universe to ensure we don't have any discontinuity effects). Actually forget single galaxies they are probably insignificant!

Turns out detailed simulations are extremely difficult. The Millennium Run simulation remains one of the largest such simulations performed, and there are a number of things it simply wasn't able to simulate due to computing limitations. This was a dark matter only simulation.

Since then, most of the work seems to have been in the direction of attempting to incorporate the dynamics of normal matter into the simulations, which turns out to be extraordinarily difficult. To get the right answer for galaxies, you have to simulate such things as:

1. Galactic magnetic fields. These magnetic fields tend to be exceedingly complicated and affect the flows of ionized gases.
2. Supernovae. Supernovae seed metal throughout galaxies and have significant impacts on star formation rates.
3. Star formation. We have to get a good handle on the variables affecting star formation, as we can't simulate the formation of each and every star in a 100,000,000,000 star galaxy.
4. Supermassive black holes. The supermassive black holes at the centers of galaxies are huge engines driving tremendous changes throughout the galaxy. It is often believed, for instance, that the behavior of the supermassive black hole at the center of the galaxy is, by large, responsible for whether a galaxy relaxes into a spiral or a spheroidal shape.

These are just a few off the top of my head. This is a bit outside my field, so I'm sure I missed a few things, but hopefully this gives you a vague idea that this is just a very difficult problem.

 

[TrickyDicky]

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.

Actually, we won't "know" what the case is until we gather more observational info, that's the point here, and fortunately it seems it might be a relatively short time until we can tell, we are already reaching the threshold of the 100 Mpcs, and the limit of 200 Mpcs proposed in the paper I linked seems reasonable and it might not take as many years as it has taken to get near the 100 Mpcs.
It feels great when empirical observations needed to confirm or falsify a theoretical model seem so near and are not subject to different interpretations (provided a big enough sample of galaxies), that's a situation so infrequent in cosmology!

 

[Tanelorn]

Thanks for reply Chalnoth. If it is as complicated as you say and we can't right down a model that can be verified by simulation then it must be very difficult to beleve that we even have a standard model? However perhaps I am wrong when you consider that we can't even accurately predect the weather or the climate yet we think we understand these.

 

[inflector]

I've been thinking about the OP again:

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.

This strikes me as a very insightful indictment of the cosmological principle itself as it is interpreted by most.

The principle states that there are no preferred locations and directions in the universe yet the principle is violated at every scale we can measure. As someone who is only recently studying cosmology and the issues involved, this strikes me as the wrong conclusion. This could simply be because I misunderstand the meaning of the principle. Or perhaps it is indicative of where we are in the progression of our evolution of theory.

As a neophyte, I ask myself: how can one of the major assumptions of standard cosmology be contradicted at every level of our empirical observation yet it still remains "valid?"

I found marcus's quote interesting and perhaps illustrative of the issue raised in the OP:

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.

[second bold section is mine, the bold of "effective" was in marcus's post]

So it seems to me that the assumption that whatever is out beyond what we can see is "enough like what we can see" seems intuitively obvious as a decent starting place for assumptions about what we cannot see. It sure makes a lot more sense than assuming that it's filled with dragons or turtles or something we have never seen. It might not hold, but it sure seems like a good starting assumption.

Interestingly, the real question is what this idea of "enough like what we can see" really means. I can see two different directions that one can take this:

1) Statistical Similarity - Assuming that the density and other characteristics that we can measure represent the space outside our horizon. This is the approach that I believe cosmology takes with the cosmological principle.

2) Fractal Continuation - Assuming that the progression of fractal structure that we see starting with quarks in nucleons, to nucleons in atoms, to atoms in molecules, to atoms and molecules in plants and animals and planets and stars, to planets in solar systems, to stars in galaxies, to galaxies in clusters, to clusters in superclusters and filaments, ... assuming that this progression continues, which means that we are very likely to find continued fractal structure as we look out further and therefore it is unlikely that we'll just happen to be in the center of some uniform density system even at the largest scales.

So in both cases, similarity is being projected out beyond what we can see. In the first case, we assume that things smooth out despite our not seeing smoothness in our observations except at very narrow bands of observation. In the second case, we assume that we will see more fractal clumping and bunching of matter which matches the character of what we see.

I don't understand why the second perspective is not more widely held.

The first perspective seems tenable only in the realm where our instruments just happen to detect similarity at the boundaries, but how often has that been true even in the history of cosmology? To me, it doesn't even seem to be true now?

At first, when we only saw the stars, we were in the center of our universe. Then a bit later we once saw only the milky way as our universe, and we were on the bare edge of it. Later we came to see the galaxies as the dominant feature of the universe. But how do we really know that we are not missing as much as we once did when we only saw the Milky Way and didn't realize that some of the stars we saw were actual galaxies?

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.

That sure seems to me to be a better assumption. It fits the facts better.

 

[TrickyDicky]

I've been thinking about the OP again:


This strikes me as a very insightful indictment of the cosmological principle itself as it is interpreted by most.

The principle states that there are no preferred locations and directions in the universe yet the principle is violated at every scale we can measure. As someone who is only recently studying cosmology and the issues involved, this strikes me as the wrong conclusion. This could simply be because I misunderstand the meaning of the principle. Or perhaps it is indicative of where we are in the progression of our evolution of theory.

As a neophyte, I ask myself: how can one of the major assumptions of standard cosmology be contradicted at every level of our empirical observation yet it still remains "valid?"

I found marcus quote interesting and perhaps illustrative of the issue raised in the OP:

[second bold section is mine, the bold of "effective" was in marcus' post]

So it seems to me that the assumption that whatever is out beyond what we can see is "enough like what we can see" seems intuitively obvious as a decent starting place for assumptions about what we cannot see. It sure makes a lot more sense than assuming that it's filled with dragons or turtles or something we have never seen. It might not hold, but it sure seems like a good starting assumption.

Interestingly, the real question is what this idea of "enough like what we can see" really means. I can see two different directions that one can take this:

1) Statistical Similarity - Assuming that the density and other characteristics that we can measure represent the space outside our horizon. This is the approach that I believe cosmology takes with the cosmological principle.

2) Fractal Continuation - Assuming that the progression of fractal structure that we see starting with quarks in nucleons, to nucleons in atoms, to atoms in molecules, to atoms and molecules in plants and animals and planets and stars, to planets in solar systems, to stars in galaxies, to galaxies in clusters, to clusters in superclusters and filaments, ... assuming that this progression continues, which means that we are very likely to find continued fractal structure as we look out further and therefore it is unlikely that we'll just happen to be in the center of some uniform density system even at the largest scales.

So in both cases, similarity is being projected out beyond what we can see. In the first case, we assume that things smooth out despite our not seeing smoothness in our observations except at very narrow bands of observation. In the second case, we assume that we will see more fractal clumping and bunching of matter which matches the character of what we see.

I don't understand why the second perspective is not more widely held.

The first perspective seems tenable only in the realm where our instruments just happen to detect similarity at the boundaries, but how often has that been true even in the history of cosmology? To me, it doesn't even seem to be true now?

At first, when we only saw the stars, we were in the center of our universe. Then a bit later we once saw only the milky way as our universe, and we were on the bare edge of it. Later we came to see the galaxies as the dominant feature of the universe. But how do we really know that we are not missing as much as we once did when we only saw the Milky Way and didn't realize that some of the stars we saw were actual galaxies?

That sure seems to me to be a better assumption. It fits the facts better.

But once again you have to understand that the assumption that seems better to you for the reasons you explain and that seems pretty logical is not compatible with standard cosmology and here enter "extra-scientific" factors that pertain to the sphere of human psychology. So you need huge evidences to change a paradigm that is believed to be true by most of the comunity, because the emotional anchor with the current paradigm is very strong.
On the other hand when you interpret observations in a way different than the standard model, you better bring with you a new model that is internally consistent, and also consistent with the laws and theories of physics and that explains at least as much and predicts at least as much as the model you're questioning, otherwise the practical thing for mainstream science is to basically ignore the alternative interpretation, and I think that is fair enough even if sometimes in forums it gets a little overacted.
The situation changes a little when you actually find overwhelming observations that contradict the paradigm, but that is not the case yet, and still if that were to happen you still need a viable alternative model that fits the new observations and the old ones.

 

[tom.stoer]

The principle states that there are no preferred locations and directions in the universe yet the principle is violated at every scale we can measure.

...

I can see two different directions that one can take this:

1) Statistical Similarity - Assuming that the density and other characteristics that we can measure represent the space outside our horizon. This is the approach that I believe cosmology takes with the cosmological principle.

2) Fractal Continuation - Assuming that the progression of fractal structure that we see ... assuming that this progression continues, which means that we are very likely to find continued fractal structure as we look out further ...

So in both cases, similarity is being projected out beyond what we can see. ...

I don't understand why the second perspective is not more widely held.

Inflector, thanks for the excellent summary of my thoughts; seems that you understand better than myself :-)

That sure seems to me to be a better assumption. It fits the facts better.

What I learned during this discussion is that I am certainly not the first one who had these ideas. Perhaps my idea that large-scale fractal-like structures have not been formed during expansion by gravitational attraction (which seems to be impossible) but may be relicts from a kind of phase transition (which might be a rather hasty conclusion) is new. But that was not my original intention. Instead it was mainly about asking how structures could continue beyond the observable universe and if and how structures on an these scales can cause physical effect within the visible universe.

From what I learned this discussion is already a few years old - and the interpretation of the data is by no means undisputed!

I skimmed through some papers trying to explain accelerated expansion via large inhomogenities and a violation of the cosmological principle in the sense that the solar system is in a rather special location. Btw.: I don't think that this idea has already been disproven (nor has it been proven):
a) both proponents and opponents do have not enough data and facts available to settle the discussion conclusively
b) the discussion regarding the cosmological principle strikes me as the same facts seem to allow two contradictory interpretations

The problem seems to be that beyond a certain scale the universe we see is too young to allow for bright structures like galaxies to be observed (as they have not been formed since the big bang). So instead using facts to derive conclusions regarding the large scale structure it may very well be that the only option we have is to find a natural principle w/o being able to give a sound proof. My claim is simply that - given that the two options just discussed cannot be decided experimentally - we have to discuss whether such a principle is natural.

From what I know and from what I see it is by no means clear that the cosmological principle as we know it today is the only natural principle one can imagine.

 

[tom.stoer]

@TrickyDicky: most of your arguments are based on "what is believed to be true by most of the comunity" and on an "emotional anchor". I think this is not a very good reason to believe in a scientific theory.

The standard model of cosmology has some severe shortcomings:

• it is to a very large extend based on invisible and poorly understood entities like dark matter and dark energy
• it seems to be the case that interpretation of data is by no means unambiguous
• it uses a principle that is simply wrong on the accessible scales and can perhaps be saved on scales that may never be accessible to observations

The starting point for scientific revolutions was never a new, internally consistent model; it was quite often "only" reasonable doubt about common belief; only years later these new models emerged and were widely accepted (quantummechnaics, general relativity)

My conclusion is that it is much too early to scrap the cosmological standard model - but it's never too early to challange it!

 

[inflector]

What I learned during this discussion is that I am certainly not the first one who had these ideas. Perhaps my idea that large-scale fractal-like structures have not been formed during expansion by gravitational attraction (which seems to be impossible) but may be relicts from a kind of phase transition (which might be a rather hasty conclusion) is new. But that was not my original intention. Instead it was mainly about asking how structures could continue beyond the observable universe and if and how structures on an these scales can cause physical effect within the visible universe.

[SNIP]

The problem seems to be that beyond a certain scale the universe we see is too young to allow for bright structures like galaxies to be observed (as they have not been formed since the big bang). So instead using facts to derive conclusions regarding the large scale structure it may very well be that the only option we have is to find a natural principle w/o being able to give a sound proof. My claim is simply that - given that the two options just discussed cannot be decided experimentally - we have to discuss whether such a principle is natural.

From what I know and from what I see it is by no means clear that the cosmological principle as we know it today is the only natural principle one can imagine.

You bring up an interesting point. One of the reasons that this thread caught my interest was because of the tie-in between quantum gravity and cosmology. My personal research in this area is exploring the nature of spacetime structure and gravity at the extremes: both the cosmological and quantum scales, and less-popular theories for these domains.

I believe that a valid quantum gravity theory, if found, should shed some light on this issue of whether or not fractal structure or homogeneity dominates cosmology outside the horizon. If, for example, it could one day be shown that spacetime itself has a fractal structure on the quantum scale, and it could be demonstrated that this fractal nature also was the basis for the fractal structure at larger scales, then it would certainly be reasonable to conclude that fractal structure continued out beyond the cosmological horizon.

 

[Chalnoth]

Actually, we won't "know" what the case is until we gather more observational info, that's the point here, and fortunately it seems it might be a relatively short time until we can tell, we are already reaching the threshold of the 100 Mpcs, and the limit of 200 Mpcs proposed in the paper I linked seems reasonable and it might not take as many years as it has taken to get near the 100 Mpcs.
It feels great when empirical observations needed to confirm or falsify a theoretical model seem so near and are not subject to different interpretations (provided a big enough sample of galaxies), that's a situation so infrequent in cosmology!

We already have measurements that confirm the standard model at length scales much, much greater than 100Mpc, such as CMB studies, baryon acoustic oscillation studies, and supernova studies.

 

[Chalnoth]

Thanks for reply Chalnoth. If it is as complicated as you say and we can't right down a model that can be verified by simulation then it must be very difficult to beleve that we even have a standard model? However perhaps I am wrong when you consider that we can't even accurately predect the weather or the climate yet we think we understand these.

The key is focusing primarily on areas where we can do the calculations. Basically, on large length scales, we can make certain approximations to the behavior of gravity that allows us to calculate things to high accuracy. In this regime, where we can be most sure of systematic errors, our simplest models match reality excellently.

 

[TrickyDicky]

@TrickyDicky: most of your arguments are based on "what is believed to be true by most of the comunity" and on an "emotional anchor". I think this is not a very good reason to believe in a scientific theory.

That is exactly my point, that majority belief and emotional factors are not scientific reasons to support a theory.

The standard model of cosmology has some severe shortcomings:

• it is to a very large extend based on invisible and poorly understood entities like dark matter and dark energy
• it seems to be the case that interpretation of data is by no means unambiguous
• it uses a principle that is simply wrong on the accessible scales and can perhaps be saved on scales that may never be accessible to observations

The starting point for scientific revolutions was never a new, internally consistent model; it was quite often "only" reasonable doubt about common belief; only years later these new models emerged and were widely accepted (quantummechnaics, general relativity)

My conclusion is that it is much too early to scrap the cosmological standard model - but it's never too early to challange it!

I basically agree with the shortcomings you list and your conclusion, just a couple of remarks, GR in its November 1915 form was new and internally consistent, not only that, it made accurate predictions and had a tremendous explanatory power based in the geometrical concept of curvature, it fulfilled all the demands I asked of new revolutionary theories to overcome resistance to change, it actually became accepted almost inmediately, even if it corrected no other than Newton.
In the case of QM in its 1926 version was also pretty much giving predictions and explaining results. So certainly in the two cases you cite the starting point was indeed a new and internaly consistent theory.
So I was just warning challengers about the difficulty of the task.

We already have measurements that confirm the standard model at length scales much, much greater than 100Mpc, such as CMB studies, baryon acoustic oscillation studies, and supernova studies.

Those are very much open to different interpretations(meaning their interpretation is heavily model dependent), and BAO measurements are being questioned even in the mainstream journals.
Whilst the statistical treatment of the data recovered from redshift surveys has been pretty much agreed upon by the main competitor teams (orthodox cosmology-Peebles, Hogg etc- and Fractal cosmology team-Pietronero,Joyce, Baryshev,etc..). And therefore is less subject to model dependent interpretatons.

 

[Chalnoth]

Those are very much open to different interpretations(meaning their interpretation is heavily model dependent), and BAO measurements are being questioned even in the mainstream journals.
Whilst the statistical treatment of the data recovered from redshift surveys has been pretty much agreed upon by the main competitor teams (orthodox cosmology-Peebles, Hogg etc- and Fractal cosmology team-Pietronero,Joyce, Baryshev,etc..). And therefore is less subject to model dependent interpretatons.

The disputes of these measurements are all about the details, not the overall results. And it's really not reasonable for so many such extremely different measures to have all converged on the same cosmology if that cosmology wasn't, at least to a decent approximation, largely accurate.

 

[tom.stoer]

... just a couple of remarks, GR in its November 1915 form was new and internally consistent, not only that, it made accurate predictions and had a tremendous explanatory power based in the geometrical concept of curvature, it fulfilled all the demands I asked of new revolutionary theories to overcome resistance to change, it actually became accepted almost inmediately, even if it corrected no other than Newton.
In the case of QM in its 1926 version was also pretty much giving predictions and explaining results. So certainly in the two cases you cite the starting point was indeed a new and internaly consistent theory.

No, that is not what I wanted to say:
The story of GR did not start in 1915, it started in 1905 or soon after. It was clear for Einstein - and for the whole communty - that SR is a challenge for Newtonian gravity and that not both can be "true" but it took approx. ten years to present the final result.
The same applies to QM: the story started approx. in 1905 (or even earlier) and it took approx. 20 years to find a consistent andpredictive theory. So over 20 years the communty new that what was available (Bohr, Bohr-Sommerfeld, ...) was essentitally "wrong".

The development of QM was deeply rooted in reasonable doubts. Therefore it's absolutely legitimate to provide and discuss good reasons why certain assumtions or theories may be "wrong" w/o being able to provide a theory that is "right". It's this discourse that is required in order to make progress; w/o questioning the principles of theories science becomes religion.

My observation is that b/c of lack of sufficient experimental support in certain regimes (quantum gravity / string theory, cosmology) these discussions are more importent than ever.

 

[Chalnoth]

My observation is that b/c of lack of sufficient experimental support in certain regimes (quantum gravity / string theory, cosmology) these discussions are more importent than ever.

Well, one of the problems is that without the experimental support in regimes beyond the standard model, there really hasn't been any clear direction on where to go, so theorists have just been branching out more or less blindly in a tremendous variety of directions. Sadly, it's going to be nigh impossible to distinguish the correct theories from the incorrect ones until we start producing experiments that clearly and unambiguously deviate from our current theories. The problem is that those places where we may see some deviation all lie in regimes where systematic uncertainties are still quite high, so unfortunately we can't be sure just yet that we have seen any deviation.

 

[tom.stoer]

In principle you are right, but my claim is that regarding the cosmological principle these deviations are there (!) and can only be explained away by referring to scales beyond the observable universe. Of course systematic and statistical uncertainties exist, but they exist regardless if you want to prove the standard model or if you want to disprove it. The problems are equally severe for all reserach directions.

 

[Chalnoth]

In principle you are right, but my claim is that regarding the cosmological principle these deviations are there (!) and can only be explained away by referring to scales beyond the observable universe. Of course systematic and statistical uncertainties exist, but they exist regardless if you want to prove the standard model or if you want to disprove it. The problems are equally severe for all reserach directions.

What deviations? Where the cosmological principle is concerned, the large-scale experiments confirm expectations to a very high degree of accuracy. There are some interesting hints in some places that maybe there might be something interesting going on, but so far we don't know for sure whether it's an experimental/observational problem or something we don't understand about fundamental physics that is causing the discrepancy.

 

[tom.stoer]

What deviations?

The deviations of matter distribution (clusters, voids, ...), the deviations of the CMB from a perfect monopole profile.

Where the cosmological principle is concerned, the large-scale experiments confirm expectations to a very high degree of accuracy.

You can interpret the data in that way if you like; but you always refer to the idea that homogeneity will hold on scales beyond the observed scales. So you may use homogeneity as an element of your model, but it's certainly an input which cannot be confirmed experimentally. All measurements taken so far show direct evidence that visible matter is not distributed homogeniously (clusters, voids, ...). The CMB is not homogenious, either (higher multipoles) [there are even indications that there might be a small anisotropy in both matter flow and CMB. ]

The claim that homogeneity holds must always refer to scales larger than the observed ones and will therefore always make assumptions how matter distribution will continue outside the directly visible domain.

So this "confirmation" of the cosmological principle always assumes that it may hold outside the visible universe - and is therefore not a confirmation.