Does the expansion rate of our universe depend on its mean density?

[MathematicalPhysicist]

What methods are there to figure out if our universe has a boundary or not?
And if it does are we living on the boundary (like in the case of our Earth that we live on a sphere and not inside the earth)?

 

[Wallace]

From observations we know that the visible universe has no 'boundary' in the sense that it is (statistically) the same everywhere in terms of the average density of matter etc. Beyond the observable universe we cannot say, although our theories strongly suggest that there cannot be a boundary beyond the observable universe either.

 

[George Jones]

Another possible and very speculative take on the original post is "Do we live on a brane?"

I don't know anything about either the theory behind this or the predictions (if any) of this scenario. At least one GR/cosmology book

https://www.amazon.com/dp/0387691995/?tag=pfamazon01-20

has a chapter (17 Brane-Worlds) on this.

 

[Chronos]

The universe appears to have an observational boundary. Most astrophysicists are not terribly interested in what may lay beyond. It is untestable.

 

[MathematicalPhysicist]

Why is it untestable?

If it's because no light can come from beyond the observed universe, then I might say that also dark matter hypothesis isn't testable, it doesn't interact with our ordinary matter and light, how can we test it?

 

[Wallace]

Why is it untestable?

If it's because no light can come from beyond the observed universe, then I might say that also dark matter hypothesis isn't testable, it doesn't interact with our ordinary matter and light, how can we test it?

Not at all. The only reason we think DM exists is beacuse we have seen things that suggest it probably does. We observe the gravitational influence that it has on many different types of observable things.

On the other hand, by definition anything outside the observable Universe cannot have a causal influence on anything that we can see. Hence we cannot claim to be able to test a hypothesis related to such regions.

 

[Chronos]

Affirming Wallace, we have an abundance of observational evidence supporting the existence of dark matter going all the way back to Zwicky. Not having detecting it is our problem, not that of the universe. Dirac predicted neutrinos long before we figured out how to detect them and DM is even more exotic than neutrinos. I think we will figure it out within 10 or so years.

 

[MathematicalPhysicist]

As far as I remember astronomers had believed that there should be some relation between the mass of the universe and its displacement r, I don't quite recall what behaviour it should be.
But they found from observations that such relation doesn't occur, so they had to fix it, so some correct it by adding a new material, called dark matter, and others like Milgrom say that something is not perfect with our models at long distances, so let's modify it by MOND.
Now I don't see how something which is beyond the observable universe, by observable I guess you mean by light and its interaction with matter, mustn't have a causal effect on the observable universe, if you can't observe it doesn't mean it doesn't affect us, all we can say what is beyond the observed universe we can't know anything of it, but as far as we can tell it may or it may not affect us, perhaps it's unscientific question to ask what is beyond the observed universe if you can't observe it.

 

[Wallace]

As far as I remember astronomers had believed that there should be some relation between the mass of the universe and its displacement r, I don't quite recall what behaviour it should be.
But they found from observations that such relation doesn't occur, so they had to fix it, so some correct it by adding a new material, called dark matter, and others like Milgrom say that something is not perfect with our models at long distances, so let's modify it by MOND.

Back up, you're comparing apples with cucumbers here. It was found that the motions of stars in any given galaxy in inconsistent with the visible mass of that galaxy, hence the inclusion of dark matter. Note that there are many other reasons to include dark matter in the model, this was just the first indication (techincally the first indication was by Zwicky in clusters as Chronos mentioned, but that was ignored for a low time).

Anyway, none of this has anything to do with the mass of the Universe. In your first sentence you need to replace 'Universe' with 'galaxy'. These are quite different things!

Now I don't see how something which is beyond the observable universe, by observable I guess you mean by light and its interaction with matter, mustn't have a causal effect on the observable universe, if you can't observe it doesn't mean it doesn't affect us, all we can say what is beyond the observed universe we can't know anything of it, but as far as we can tell it may or it may not affect us, perhaps it's unscientific question to ask what is beyond the observed universe if you can't observe it.

By definition the observable universe demarcates those regions for which light has been able to reach us since the Big Bang. Hence by definition anything outside of this is not causally linked to us, since nothing (including graviational changes etc) travels faster than light. The observable Universe doesn't refer just to things we have seen, it refers to regions that causality allows us to potentially see, regardless of whether or not our view of some part is obscured for some reason.

 

[S.Vasojevic]

By definition the observable universe demarcates those regions for which light has been able to reach us since the Big Bang. Hence by definition anything outside of this is not causally linked to us, since nothing (including graviational changes etc) travels faster than light. The observable Universe doesn't refer just to things we have seen, it refers to regions that causality allows us to potentially see, regardless of whether or not our view of some part is obscured for some reason.

One question. When you throw expanding geometry in picture, does that mean that what is not casually linked to us now, will never be linked?

 

[Wallace]

It turns out you need to know more than just that the Universe is expanding to answer that question. If the Universe contained only matter, such that is always deccelerated, it turns out that any region will at some point be 'observable'. On the other hand, in the case where the Universe continues to accelerate in the future (such as we think we will do) then there is a finite region of the universe that will ever be observable, even given a infinite amount of time.

I think this is best understood using space-time diagrams employing the conformal time, where you can map an infinite future onto a finite graph. There are some in papers by Davis & Lineweaver that show this, though there are probably some better references or websites that go through this in some detail. Maybe someone else knows a good link?

 

[S.Vasojevic]

And then comes superluminal question. If most distant galaxies in our OU recede faster than light, are they 'leaving' casual connection with us, or is it safe to say that they are not going faster then light at that distance, as you suggested earlier in one of your posts?

 

[Ich]

Maybe someone else knows a good link?

I'd say Ned Wright's site is better.

 

[Wallace]

I was waiting for that :) [Edit: that refers to S.Vasojevic post, not Ich's]

Remember that you can only talk about superluminal speed in a particular instantaneous rest frame. The only speed limit in GR is that light moves faster than anything else in any given rest frame. So, a galaxy that we previously did see photons from, that we now cannot see photons from is not moving away from us at faster than light, because it is always moving slower than the light in its rest frame. That's the only sensible way you can define 'faster than the speed of light'.

Note that the reason we can't ever see photons from regions beyond a certain radius cannot be properly understood through how fast a galaxy is moving, but through how rapidly it is accelerating. It's acceleration that shuts off regions from our future light cone, not motion.

 

[S.Vasojevic]

So there are regions which are leaving our observable world?

Or to jump to the point of my questions, which one is true, if you take that expansion is accelerating:

1. OU is staying as it is, just expanding through space.
2. OU is gaining content.
3. OU is loosing content. One day there will be nothing to observe.

 

[Wallace]

So there are regions which are leaving our observable world?

Or to jump to the point of my questions, which one is true, if you take that expansion is accelerating:

1. OU is staying as it is, just expanding through space.
2. OU is gaining content.
3. OU is loosing content. One day there will be nothing to observe.

It depends on how you define things. Take your point 3. If you have a set of galaxies, each one a bit further from the other, then over time you would slowly see them fade away one by one, starting from the furthest one away. In this sense, the OU is 'losing content' and eventually all of those galaxies will be unobservable. The important caveat is that those galaxies are in the Hubble flow to being with; the local group is not expanding because it represents a region that had sufficient density to collapse and virialise, so we will always be able to see the galaxies in our local group (ignoring phantom dark energy models, which everyone should do!).

I can't think of a way to define things to make your point 2 a correct description, but you could argue for point 1. It turns out that a universe dominated by a cosmological constant is actually a static solution, it has no time dependance. It's a bit of a pedantic point though, requiring some jiggery-pokery to demonstrate this starting from the FRW metric, so your point 3 is probably the simplest way to think of it.

 

[S.Vasojevic]

Is there any importance in that towards the gravitational behavior on large scale?
It seems to me that if there is a constant drop of mass that is casually connected to us, then accelerated expansion should result with more acceleration, which further speeds up mass 'disconnection', which again results with more acceleration. Kind of 'runaway' process.

 

[Wallace]

Well it is a runaway model in a sense, as matter becomes more diluted the cosmological constant becomes more dominant, increasing the acceleration rate, which dilutes matter faster...

The causal part is a red herring in that though, it just comes about due to the change in the mean density, which is precisely the same everywhere in the idealised homogeneous model. In an FRW universe you can always use a Gauss's law type argument and only consider a finite radius around you and make the assumption that everything outside of that is a empty. No matter what radius you choose for this, you will always get the same answer for the expansion rate. This shows that the only things that matters is the mean density.