Is the Big Bang Expanding into a Preexisting Void?

[twofish-quant]

If WE, and everything we see came from the same point and the same time, then wouldn't it make sense to expect it all to look the same in every direction?

Only if you happen to be lucky enough to be near the center of the explosion, and that is a very weird coincidence. If all of the places in the universe that you happen to end up, how is it that you ended in the middle?

 

[twofish-quant]

If you go back to the original source "Relativity, Gravitation, and World Structure" you will see that Milne's model described a Big Bang expanding into a preexisting void.

And if you go back to that era, you will find that it's only one of about a dozen ideas that people had that made perfect sense with the data that they had available. Something that I like students to do is to look at old scientific papers and see what they were arguing about at some decade. The reason for this is that the way that we look at people in the 1930's is how people are going to look at us in the 2050.

Personally, if I had been around in 1960, I would have been a strong opponent of big bang because its much less elegant than steady-state. Looking the arguments, I probably would have considered the first measurements of CMB in 1965 to be experimental errors (and there were lots of reasons to think that they would have been wrong) and I probably wouldn't have been converted until the early 1970's.

I wouldn't be terribly surprised if five years from now, someone quotes me bashing Webb's results on the changing fine structure constant which will be standard knowledge at that time.

As far as the justification for rejecting the Milne model, I have been trying to figure that out as well.

It doesn't fit the data. People have been extremely patient explaining why it doesn't fit the data.

Unfortunately, the few remaining copies of Relativity Gravitation and World Structure are probably to be burned, and the idea, whether correct or not, will be forever lost.

If it's right, then people will stumble on it in the end. Continental drift and black holes were two ideas that were dormant for decades before someone observed something. Also scientists are more open minded that I think you give them credit for.

 

[twofish-quant]

For now, the only variation from place to place that we have at least some confidence of is the electroweak symmetry breaking event, which appears to have a particular parameter that is random and varies from place to place (as in it is likely different some place far from our observable universe, but is the same everywhere we can see).

This particular parameter is the fine structure constant which happens to be set to 1/137.(something) which is a number that looks pretty random. There are a number of experiments trying to see if the fine structure constant varies over space and time. One group has reported yes. Everyone else has reported no, and the details are in another thread on this forum.

 

[Chalnoth]

This particular parameter is the fine structure constant which happens to be set to 1/137.(something) which is a number that looks pretty random. There are a number of experiments trying to see if the fine structure constant varies over space and time. One group has reported yes. Everyone else has reported no, and the details are in another thread on this forum.

Actually, no, I wasn't talking about the fine structure constant, but rather the weak mixing angle. I don't think we have any indication that the fine structure constant could be different from place to place, but as I understand it the weak mixing angle is expected to be a result of a spontaneous symmetry breaking event, which would produce different angles in different locations (though it is definitely the same everywhere within our observable universe).

 

[twofish-quant]

When it comes to beginnings, some are better than others - but there is not much possibility of being proved wrong even if your ideas are as far out as mine.

Which is why I find this sort of thing surprisingly uninteresting. What happens at t=0 is rather uninteresting to me because you can basically make up anything and there is nothing that can prove you wrong.

This is not true for events at t=3 million years or t=3 minutes. At t=0 you can argue that some giant multidimensional space bird laid an egg that turned into the universe. At t=3 minutes, the temperatures are those that we can simulate in nuclear reactors. So you have to ask why you don't see space birds popping out of fusion reactors. At t=3 million years, you have to ask why you don't see space birds everywhere. There is a boundary point right now, at which if there is a giant space bird, then you such see it with the LHC.

At t=0, you don't know when something strange is happening because everything is strange. That's not true for t=3 million years, so when you see bricks start levitating themselves, then you know something odd is going on.

I'm a little puzzled why people are so fascinated with t=0, and its a religious, cultural and historical thing. Personally, I'm more interested in the "dark ages."

 

[Chalnoth]

I think it's precisely because it's rather wide-open that people want to talk about it so much: people don't have to actually know anything to say something about what's going on. But when you get into the later universe, we know quite a lot, and just pulling random ideas out of your backside starts to be directly contradicted by experiment. Actually presenting something potentially interesting requires knowledge and serious thought. So I think most people get rapidly discouraged when they get into the areas where we do have ample experimental knowledge.

Of course, we do regularly get people who are genuinely interested in the areas where we know more as well. So it isn't quite so bad as all that.

 

[twofish-quant]

I don't think we have any indication that the fine structure constant could be different from place to place, but as I understand it the weak mixing angle is expected to be a result of a spontaneous symmetry breaking event, which would produce different angles in different locations (though it is definitely the same everywhere within our observable universe).

My (possibly incorrect) understanding is that the fine structure constant also arises from the same spontaneous symmetry breaking event as the weak mixing angle, and so it's likely to be random for the same reasons. This is why people have suddenly got interested in anthropic arguments because with the current state if HEP, the fine structure constant is basically a totally random value.

Also the reason that people like cosmic inflation is that it provides an explanation for why the universe seems to look the same. What happened was that during and after the SSB event, the universe expanded so much that places with different values of the fundamental constants become unobservable.

 

[Chalnoth]

My (possibly incorrect) understanding is that the fine structure constant also arises from the same spontaneous symmetry breaking event as the weak mixing angle, and so it's likely to be random for the same reasons.

Hmm, that's conceivable.

Also the reason that people like cosmic inflation is that it provides an explanation for why the universe seems to look the same. What happened was that during and after the SSB event, the universe expanded so much that places with different values of the fundamental constants become unobservable.

Indeed. In fact, it seems that inflation expanded the universe so much that even defects that would have occurred from such a spontaneous symmetry breaking event are so far unobserved (namely, cosmic strings).

 

[twofish-quant]

Hmm, that's conceivable.

Did some more research on this. It turns out that the fine structure constant is believed to result from broken symmetry at the energies that strong and electroweak forces unify. This is different from the weak mixing angle which happens when EM and the weak forces unify. The latter are energies we can do direct experiments on.

The other interesting thing is that it turns out that we can do lab experiments to show that the fine structure constant isn't constant. As energy increases there are vacuum effects that change the value of the fine structure constant.

Indeed. In fact, it seems that inflation expanded the universe so much that even defects that would have occurred from such a spontaneous symmetry breaking event are so far unobserved (namely, cosmic strings).

One consequence of inflation is that the unobserved universe is a lot, lot bigger than the observed universe. You can get a limit for the size of the unobserved universe. You figure out how many cosmic strings you are likely to generate, you see how much you have to inflate the universe so that you don't see any. That gives you a bound as to how much of the universe is unobserved.

 

[Chalnoth]

Did some more research on this. It turns out that the fine structure constant is believed to result from broken symmetry at the energies that strong and electroweak forces unify. This is different from the weak mixing angle which happens when EM and the weak forces unify. The latter are energies we can do direct experiments on.

That makes a lot of sense, and it's why I wouldn't go so far as to say we (yet) have good reason to believe that the fine structure constant varies from place to place in the universe. Granted, I think it's highly likely, I'm just not so sure that we're there yet in terms of observation.

The other interesting thing is that it turns out that we can do lab experiments to show that the fine structure constant isn't constant. As energy increases there are vacuum effects that change the value of the fine structure constant.

It's been a little bit since I've looked into this, but from what I understand, this variation is largely understood, and doesn't constitute an actual variation of the coupling constant, but instead some "effective" variation. I'm not entirely certain what this means, but I gather that you can wrap some of the terms in higher-energy interactions back into the strength of the interaction, allowing coupling constants to run with energy.

The effect of this, it turns out, is that at some rather high energy, the variation of these effective coupling constants for the strong, weak, and electromagnetic forces tend towards close to the same value. If we add supersymmetry to the mix, the alignment between the coupling constants at high energy is much better.

One consequence of inflation is that the unobserved universe is a lot, lot bigger than the observed universe. You can get a limit for the size of the unobserved universe. You figure out how many cosmic strings you are likely to generate, you see how much you have to inflate the universe so that you don't see any. That gives you a bound as to how much of the universe is unobserved.

Well, at lower bound, at least! I don't think you could, even in principle, obtain an upper bound from this because this only estimates the amount of expansion after the symmetry breaking event, while there could in principle have been quite a lot of expansion before that event.

 

[JDoolin]

Only if you happen to be lucky enough to be near the center of the explosion, and that is a very weird coincidence. If all of the places in the universe that you happen to end up, how is it that you ended in the middle?

Quite the contrary. That is no coincidence at all. Every particle in the system is, in its original trajectory, in the center of the explosion.

What is your velocity? In your own reference frame, your velocity is zero. The particles around you have velocities anywhere from zero to the speed of light. Therefore no matter which particle you pick, it is going to be approximately in the center.

This is basic relativity. Think about it.

 

[Chalnoth]

Quite the contrary. That is no coincidence at all. Every particle in the system is, in its original trajectory, in the center of the explosion.

What is your velocity? In your own reference frame, your velocity is zero. The particles around you have velocities anywhere from zero to the speed of light. Therefore no matter which particle you pick, it is going to be approximately in the center.

This is basic relativity. Think about it.

Why do you continue to claim this is in any way reasonable? We've already shown that the Milne cosmology only works if the universe is completely empty. It isn't, so it's wrong.

 

[JDoolin]

If it's right, then people will stumble on it in the end. Continental drift and black holes were two ideas that were dormant for decades before someone observed something. Also scientists are more open minded that I think you give them credit for.

If you're trying to make me feel better, it's working.

But what I'd like is, even if it's wrong, for it to be properly understood, and the reasons for rejecting it to be based on actual experiment, rather than misinterpretation. I'd like to see why it's wrong.

 

[JDoolin]

Why do you continue to claim this is in any way reasonable? We've already shown that the Milne cosmology only works if the universe is completely empty. It isn't, so it's wrong.

No. You've asserted that the Milne cosmology only works if the universe is completely empty. And that was based on claiming that Milne's metric was not the Minkowski metric, which I already told you was not true.

 

[Chalnoth]

No. You've asserted that the Milne cosmology only works if the universe is completely empty. And that was based on claiming that Milne's metric was not the Minkowski metric, which I already told you was not true.

Um, no, it wasn't. It was based on the fact that the Einstein tensor vanishes with the Milne metric. The Einstein tensor also vanishes with the Minkowski metric. This changes nothing.

 

[TrickyDicky]

No. You've asserted that the Milne cosmology only works if the universe is completely empty. And that was based on claiming that Milne's metric was not the Minkowski metric, which I already told you was not true.

You seem to be muddled on this.

Let's see Minkowskian and Milne spacetimes(they are the same spacetime with a change in coordinates that shouldn't affect the physics) are both empty, meaning there is no gravity sources therefore no gravitational field. So the Milne cosmology is defined that way, as empty, and that has nothing to do with anyone's claims.

You are yourself admitting that Minkowski and Milne metrics are equivalent so you are implicitly admitting that the Milne universe is empty, so I don't know exactly where you disagree.

 

[JDoolin]

You seem to be muddled on this.

Let's see Minkowskian and Milne spacetimes(they are the same spacetime with a change in coordinates that shouldn't affect the physics) are both empty, meaning there is no gravity sources therefore no gravitational field. So the Milne cosmology is defined that way, as empty, and that has nothing to do with anyone's claims.

You are yourself admitting that Minkowski and Milne metrics are equivalent so you are implicitly admitting that the Milne universe is empty, so I don't know exactly where you disagree.

While Milne was attempting to show how ridiculous Eddington's ideas were, he gave an equation which would map comoving world-lines to world-lines that were moving away from a single event at a constant velocity. The equation was nonsense, and Milne's point was that it was nonsense.

However, because his point was also that Eddington's ideas were ridiculous, the Eddington followers latched onto the very equation that Milne was describing as nonsense, and began calling it The Milne Model.

I admit that the Minkowski metric and the real Milne metric are equivalent.

$$ds^2=dt^2-dx^2-dy^2-dz^2$$​

However when you map in the nonsense equation, and use the metric given on Wikipedia for the Milne Model:

$$ds^2 = dt^2-t^2(dr^2+\sinh^2{r} d\Omega^2)$$​

where

$$d\Omega^2 = d\theta^2+\sin^2\theta d\phi^2$$​

... this metric is no longer equivalent to the Minkowski Metric.

 

[Chalnoth]

And we're back to my previous question: why are you so absurdly opposed to a simple change of coordinates?

 

[TrickyDicky]

However when you map in the nonsense equation, and use the metric given on Wikipedia for the Milne Model:

$$ds^2 = dt^2-t^2(dr^2+\sinh^2{r} d\Omega^2)$$​

where

$$d\Omega^2 = d\theta^2+\sin^2\theta d\phi^2$$​

... this metric is no longer equivalent to the Minkowski Metric.

Well they are not exactly the same if that is what you mean, if you have an aesthetic repulsion towards FRW metrics applied to Milne's model (why? maybe because you see the introduction of a scale factor as artificial or arbitrary in a spacetime that is essentially static? I could understand that, but Milne actually also introduced artificially an explosion in his special relativistic universe that gave particle tests their speeds up to c) that's OK, but you must realize that physically from the point of view of these particles(from their proper time and length)the metric with the scale factor and the Minkowski metric are indeed equivalent, the Minkowski metric is called the "private" frame in Milne's universe and the FRW metric would be the "public" view as seen from an outside point of view.

 

[TrickyDicky]

Quite the contrary. That is no coincidence at all. Every particle in the system is, in its original trajectory, in the center of the explosion.

What is your velocity? In your own reference frame, your velocity is zero. The particles around you have velocities anywhere from zero to the speed of light. Therefore no matter which particle you pick, it is going to be approximately in the center.

This is basic relativity. Think about it.

This is indeed an interesting property of Milne's model shared by standard cosmology, and shows that isotropy does not necesarily always imply homogeneity, so the cosmological principle is indeed as has been said here before, a philosophical preference that ultimately will have to be confronted empirically since isotropy without homogeneity is also a possibility.

I think the key here is that our cosmology based in GR is basically telling us that there is no center( in this forum"where is the center of the universe?" is a frequent question), so no observer can be in the center, so isotropy without homogeneity doesn't imply any privileged point of view and therefore perhaps the cosmological principle is not philosophically valid in a universe ruled by the theory of relativity.

 

[Chalnoth]

This is indeed an interesting property of Milne's model shared by standard cosmology, and shows that isotropy does not necesarily always imply homogeneity, so the cosmological principle is indeed as has been said here before, a philosophical preference that ultimately will have to be confronted empirically since isotropy without homogeneity is also a possibility.

At the very least, void models to explain the accelerated expansion without any dark energy have been ruled out already:
http://arxiv.org/abs/1007.3725

I think the key here is that our cosmology based in GR is basically telling us that there is no center( in this forum"where is the center of the universe?" is a frequent question), so no observer can be in the center, so isotropy without homogeneity doesn't imply any privileged point of view and therefore perhaps the cosmological principle is not philosophically valid in a universe ruled by the theory of relativity.

Well, pretty sure that isotropy without homogeneity does imply a privileged point of view. It's just that so far there's no reason to believe our universe isn't homogeneous, as the homogeneous models work, but the inhomogeneous ones so far do not.

 

[TrickyDicky]

Well, pretty sure that isotropy without homogeneity does imply a privileged point of view. It's just that so far there's no reason to believe our universe isn't homogeneous, as the homogeneous models work, but the inhomogeneous ones so far do not.

The context of the quoted paragraph seems to indicate you meant to say does not imply.
In that case, I agree, perhaps the problem lies not in the cosmological principle in itself, which is quite reasonable and seems to agree with observation so far, but in the interpretation some cosmology books make of the principle.

 

[Chalnoth]

The context of the quoted paragraph seems to indicate you meant to say does not imply.
In that case, I agree, perhaps the problem lies not in the cosmological principle in itself, which is quite reasonable and seems to agree with observation so far, but in the interpretation some cosmology books make of the principle.

Hmm, perhaps there was some miscommunication here, as I am saying that isotropy without homogeneity does imply a privileged location.

Now, bear in mind that the statement of homogeneity is not an absolute statement. Rather it's just a statement that there is a potential choice of coordinates for which the universe appears homogeneous. If it isn't possible to select such a coordinate system, but the universe still looks isotropic to us, then that says we live in a special location.

One way to look at this is that if you can find some small number observers for whom the universe is isotropic, then the universe is also necessarily homogeneous for some choices of observers (IIRC the minimum is three non-colinear observers).

 

[TrickyDicky]

One way to look at this is that if you can find some small number observers for whom the universe is isotropic, then the universe is also necessarily homogeneous for some choices of observers (IIRC the minimum is three non-colinear observers).

How far apart would they have to be?

 

[Chalnoth]

How far apart would they have to be?

In principle any distance would do, if we're talking about a hypothetical situation where we have perfect isotropy. Clearly this isn't the case, so you'd want them to be about as far apart as is required to smooth out the small-scale fluctuations, so I'd place them at around 80Mpc or so in our universe, at a minimum.

Obviously we can't do this explicitly, but this isn't the point I'm trying to make. The point I'm trying to make is that isotropy plus no homogeneity equals a special location. The reason being that if you have isotropy at many points, you also necessarily have homogeneity. So the only way you can have isotropy and no homogeneity is if there are only a tiny fraction of the available points that have isotropy, which means that the isotropic location is a special location.

 

[TrickyDicky]

Obviously we can't do this explicitly, but this isn't the point I'm trying to make. The point I'm trying to make is that isotropy plus no homogeneity equals a special location. The reason being that if you have isotropy at many points, you also necessarily have homogeneity. So the only way you can have isotropy and no homogeneity is if there are only a tiny fraction of the available points that have isotropy, which means that the isotropic location is a special location.

Ok, unless (this is of course a thought experiment,not meant to describe our actual universe) the whole universe was bigger than the observable universe, and the 3 observers fields of view don't overlap, in that case each of them could comply with isotropy, not be in any special location wrt the total universe and this universe could be inhomogenous (but the observers would never know).

The observable part of the universe of each of these observers may or may not be itself homogenous, in case it was confirmed not to be homogenous, they could always hope that a sufficiently bigger sample of the total universe confirmed homogeneity in case it could be observed but they wouldn't be able to prove it ever since it would be outside their limit of observability.

 

[Chalnoth]

Ok, unless (this is of course a thought experiment,not meant to describe our actual universe) the whole universe was bigger than the observable universe, and the 3 observers fields of view don't overlap, in that case each of them could comply with isotropy, not be in any special location wrt the total universe and this universe could be inhomogenous (but the observers would never know).

Correct, but the point remains that it's a special position within the observable universe. That is enough, I think.

The observable part of the universe of each of these observers may or may not be itself homogenous, in case it was confirmed not to be homogenous, they could always hope that a sufficiently bigger sample of the total universe confirmed homogeneity in case it could be observed but they wouldn't be able to prove it ever since it would be outside their limit of observability.

Well, I don't think most cosmologists think that homogeneity is likely to be more correct on extremely large scales. That is, in order for a region to become nearly homogeneous, it really needs to have some time to reach some sort of thermal equilibrium. But once your distances get large enough, there won't have been any chance for such widely-separated regions to reach thermal equilibrium, and so you expect wildly different sorts of behavior.

Of course, given current observations, we expect this distance to be much larger than the size of our observable universe, but I think we expect things to get less homogeneous eventually as you go beyond our observable region.

 

[TrickyDicky]

Correct, but the point remains that it's a special position within the observable universe. That is enough, I think.

Right, it is a special location inside the observable universe since in a truly inhomogenous universe, observers on the edge of the observable universe of the original observer would probably loose the isotropy(unless isotropy lies in the eye of the observer, like beauty :) and is intrinsic to relativistic observers no matter what).
I am not sure if that is really enoug, though, as the cosmological principle is applied to the whole universe, not only to the observable part.

Well, I don't think most cosmologists think that homogeneity is likely to be more correct on extremely large scales. That is, in order for a region to become nearly homogeneous, it really needs to have some time to reach some sort of thermal equilibrium. But once your distances get large enough, there won't have been any chance for such widely-separated regions to reach thermal equilibrium, and so you expect wildly different sorts of behavior.

Of course, given current observations, we expect this distance to be much larger than the size of our observable universe, but I think we expect things to get less homogeneous eventually as you go beyond our observable region.

I tend to agree with you, but if I were to speculate about what cosmologists opine on this subject I'd say they pretty much don't think about it and when they do they favor homogeneity from a certain scale all the way to the extreme.
But the more I think of it the more convinced I am that homogeneity cannot be empirically confirmed, only suspected.

 

[Chalnoth]

But the more I think of it the more convinced I am that homogeneity cannot be empirically confirmed, only suspected.

Well, first of all, I tend to think that homogeneity should be the default assumption, because it is the simplest one in accordance with observation, and that unless pursuing an inhomogeneous universe can explain some observations, it shouldn't be considered reasonable.

One approach that has appeared recently is the attempt to explain dark energy as the result of us living in a large void. But as I linked a few posts back, this has been shown not to work when you look carefully at the details. So it seems we're back to the assumption that fits the data: homogeneity.

 

[JDoolin]

Chalnoth,

I will try to give you a demonstration of the Minkowski-Milne Model under Lorentz Transformation sometime soon.

I'm not real good with the definitions; but I think what you mean by isotropy is that it looks the same in all the directions (change theta or phi, and it looks about the same), but what you mean by homogeneity is that it looks the same at all distances, (change r, and it looks the same)

The thing is, if you ignore the relativity of simultaneity, then Chalnoth is right. Isotropy without homogeneity would imply a privileged point of view. However, if everything is flying apart from the same event, then you have to do the full analysis with the lines (or planes) of simultaneity. You'll find that every plane of simultaneity for every particle intersects the worldlines of the other particles in such a way that you DO have isotropy from the Point of View of every particle.

But you don't have homogeneity in any particle's point-of-view, because each observer sees the density tend towards infinity at the outer edge of the sphere.

Jonathan

 

[Chalnoth]

The thing is, if you ignore the relativity of simultaneity, then Chalnoth is right. Isotropy without homogeneity would imply a privileged point of view. However, if everything is flying apart from the same event, then you have to do the full analysis with the lines (or planes) of simultaneity. You'll find that every plane of simultaneity for every particle intersects the worldlines of the other particles in such a way that you DO have isotropy from the Point of View of every particle.

But you don't have homogeneity in any particle's point-of-view, because each observer sees the density tend towards infinity at the outer edge of the sphere.

This isn't what homogeneity means. Homogeneity means that if I move to a different location, I see the same thing as if I stay put.

 

[JDoolin]

This isn't what homogeneity means. Homogeneity means that if I move to a different location, I see the same thing as if I stay put.

There is some ambiguity in the statement "I move to a different location," but if we define our term "different location" to mean "landed on another inertial particle" then by your definition the Minkowski-Milne model does turn out to be both homogeneous and isotropic.

A physical change in r would represent an instantaneous change in position without changing time, or velocity. What I meant by a change in r was simply to ask what the density of particles was at a distance of r.

But you are saying you want to actually move the observer to a the new position, r. If you mean to do this literally, then you will have to increase your velocity toward the "position" where you want to go, then wait until you arrive at the "position" and then change your velocity again to stay at that "position."

This process is fairly straightforward if you have a set of comoving particles. You can take away the finger-quotes around the word "position." Since the worldlines are all parallel, the "position" as defined in the frame of the first particle, and the "position" as defined in the frame of the second particle are the same.

You will, of course, invoke the "Twin Paradox" so the traveler finds on both journeys that the particles have aged more.

However, in the Minkowski-Milne* model, an ambiguity arises; one which can be quickly cleared up by considering the intersection of world-lines, and you will need to use one of the following two definitions of position:
(1) The world-line associated with r="particle distance" which is parallel to your own, before you change velocity.
(2) The world-line of the actual particle.

And the final velocity that you wish to achieve once you get to that position could be either of the following.
(1) return to your own original velocity.
(2) match velocities with the particle and land on it.

If you use idea #1 for both, then you would not see the same thing as if you stayed put. The distribution of matter would still be a sphere, but you would no longer be in the center.

If you use idea #2, you would see essentially the same thing as if you had stayed put. You would be at the center of the sphere after you matched speed with the other particle.

Once again, accelerating and decelerating invokes the twin-paradox, but in the Minkowski-Milne model, the twin-paradox also manifests itself as "inflation" in the experience of the accelerating twin.

Jonathan

 

[Chalnoth]

There is some ambiguity in the statement "I move to a different location," but if we define our term "different location" to mean "landed on another inertial particle" then by your definition the Minkowski-Milne model does turn out to be both homogeneous and isotropic.

Yes, I would agree. The only way in which homogeneity is sensible is as statement that it is possible to choose a set of spatially-separated observers which all see the same properties of the universe. Not every potential cosmology has this property. But yes, I would agree that the Milne model does.

A physical change in r would represent an instantaneous change in position without changing time, or velocity. What I meant by a change in r was simply to ask what the density of particles was at a distance of r.

Well, there is no non-arbitrary way to connect velocities at one point with velocities at another point. So you are free to choose a different "rest" at every point in space-time, if you wish.

One way to think about it is that in General Relativity, one can move a vector at one point to another point through a method called "parallel transport". This basically consists of moving the vector along a line so that it is continuously parallel with itself. The problem is that if the space-time has any curvature, then the specific path you use to get from point A to point B changes the answer you get.

 

[TrickyDicky]

Well, first of all, I tend to think that homogeneity should be the default assumption, because it is the simplest one in accordance with observation, and that unless pursuing an inhomogeneous universe can explain some observations, it shouldn't be considered reasonable.

I agree that in practical terms the assumption of homogeneity as default makes things simpler, (the math treatment for instance) but as long as we don't have direct observations that clearly point to either homogenous or inhomogenous distribution of matter at large scales so far we just find the homogenous option more likely for philosophical, historical, model-dependent and practical reasons, not direct observational reasons, that still permit both assumptions.
When I say direct observation I mean that up to the largest range our telescopes allow currently, we haven't yet found strict homogeneity, and instead some disquieting large voids and unexpected distributions of clusters that can still be explained by statistical reasons so they don't point to an inhomogenous universe either. So it is still an open subject from the purely direct observational perspective.

Certainly, though, according to the standard model of cosmology the homogeneity assumption is mandatory and that is why we consider it as the only reasonable assumption allowed by the whole collection of observations about the universe.

For instance in an inhomogenous universe since there is no constant matter density, there is no such thing as a critical density that is ncesary to our model calculations of fundamental parameters. There wouldn't even be a mean density for the universe since it would be a function of location.

 

[Chalnoth]

I agree that in practical terms the assumption of homogeneity as default makes things simpler, (the math treatment for instance) but as long as we don't have direct observations that clearly point to either homogenous or inhomogenous distribution of matter at large scales so far we just find the homogenous option more likely for philosophical, historical, model-dependent and practical reasons, not direct observational reasons, that still permit both assumptions.

Well, I'd disagree on that. We do definitely have clear observations of isotropy. Given isotropy, we would have to live in a very special location for homogeneity to not also be true, therefore even without additional knowledge, homogeneity is very likely given isotropy.

The fact that we've been able to rule out some specific inhomogeneous models is just icing on the cake, really.

When I say direct observation I mean that up to the largest range our telescopes allow currently, we haven't yet found strict homogeneity, and instead some disquieting large voids and unexpected distributions of clusters that can still be explained by statistical reasons so they don't point to an inhomogenous universe either. So it is still an open subject from the purely direct observational perspective.

Well, obviously when we talk about homogeneity and isotropy, we're talking about statistical homogeneity and isotropy. The exact deviations from this are interesting, but don't undermine the statement that our universe is, on average, highly homogeneous and isotropic.

For instance in an inhomogenous universe since there is no constant matter density, there is no such thing as a critical density that is ncesary to our model calculations of fundamental parameters. There wouldn't even be a mean density for the universe since it would be a function of location.

Well, it's not quite that bad, because you can still talk about a mean density of the universe. This is how we deal with inhomogeneities that exist: consider the universe to be made of some mean distribution plus deviations from the mean. This separation would allow you to model any universe, in principle. The main difficulty is that the Friedmann equations start to give you the wrong answer if your universe gets too inhomogeneous.