B Is There a Model That Includes Infinite Space and Finite Matter in Our Universe?

[Mukund]

We have a Universe that can be seen by Hubble maximum and we can imagine millions time more than that but if there is no boundary, there may be another millions of universe. Suppose we gather this all millions of universe and say this is a giant universe of universes and thus matter do not stop and it goes on.
But space is there when matter is there so matter and space is related. I am in confusion over this...

 

[Nugatory]

There is one universe, and we can only see part of it. If everyone was careful about saying "the observable universe" instead of "the universe" when they meant just the part we can see, the confusion would go away.

 

[Chronos]

The prospect of a finite universe provokes silly questions like 'what lay beyond its boundary?'. Even scientists who suggest the observable universe is somehow bounded tend to concede it must be embedded in an endless collection of other finite universes. The net result being an infinite menage-iverse instead of universe, Alternatives are logically unpalatable.

 

[rede96]

The net result being an infinite menage-iverse instead of universe, Alternatives are logically unpalatable.

Accepting an infinite universe, I didn’t think there was anything that dismissed there being only a finite amount of matter within that universe. Is that the case?

 

[newjerseyrunner]

Accepting an infinite universe, I didn’t think there was anything that dismissed there being only a finite amount of matter within that universe. Is that the case?

We believe that the universe is homogeneous at those scales. We expect that if the universe is infinite, the amount of energy (matter is energy) is also infinite.

 

[PeterDonis]

Accepting an infinite universe, I didn’t think there was anything that dismissed there being only a finite amount of matter within that universe. Is that the case?

No. A spatially infinite universe containing only a finite quantity of matter would not evolve in time the way our actual universe is evolving.

 

[rede96]

No. A spatially infinite universe containing only a finite quantity of matter would not evolve in time the way our actual universe is evolving.

Our models are based on what we can observe and there is a finite amount of matter in our observable universe. So as I understand it the universe that we can observe would still evolve in time exactly the same way regardless of what is going on outside of our observable universe.

If that is the case then I don’t see how we can draw any conclusions about if there is finite or infinite amount of matter in the total universe.

 

[PeterDonis]

So as I understand it the universe that we can observe would still evolve in time exactly the same way regardless of what is going on outside of our observable universe.

This is not the case. Our observable universe is not a fixed thing; over time more of the universe becomes observable. So you can't take our observable universe at one instant and evolve it forward in time and fix the state of our observable universe at a later time. To put it another way, our observable universe at one time is not the complete causal past of our observable universe at a later time.

 

[rede96]

This is not the case. Our observable universe is not a fixed thing; over time more of the universe becomes observable. So you can't take our observable universe at one instant and evolve it forward in time and fix the state of our observable universe at a later time. To put it another way, our observable universe at one time is not the complete causal past of our observable universe at a later time.

I couldn’t argue with any of that. But the point I was trying to make, as I understand it, we don’t need to make any assumptions about what is going on outside our observable universe for our models to work for what we can see. Therefore assuming a flat specially infinite universe and that dark matter (EDIT: that was supposed to say dark energy.) is an inherent property of that flat space, it is plausible for there to be finite amount of matter but our models still describe how our observable universe will evolve over time.

I suppose another way to look at it is that scale factor *a* is arbitrary. I can bind it to any region of matter / energy filled space and it will describe how that space will evolve over time based on some initial conditions. The equations only consider what is within the initial scale factor. Or at least that’s how I understand it.

 

[PeterDonis]

we don’t need to make any assumptions about what is going on outside our observable universe for our models to work for what we can see

That's not correct. Our models model the entire universe, not just the observable universe. That's because there is no way to "cut off" the model at the boundary of the observable universe; that doesn't make physical sense. It would be like cutting off your model of the Earth's surface at your horizon; there's no reason for the Earth to just stop there.

assuming a flat specially infinite universe and that dark matter is an inherent property of that flat space

I don't know where you're getting that assumption about dark matter from. Nobody has a model in which dark matter is "an inherent property" of space, flat or otherwise. Dark matter is matter.

it is plausible for there to be finite amount of matter but our models still describe how our observable universe will evolve over time.

And this is not correct, as I've already said. A model with a finite amount of matter surrounded by emptiness out to infinity will not look, even in the observable part of it, like our observable universe actually does.

 

[PeterDonis]

scale factor *a* is arbitrary. I can bind it to any region of matter / energy filled space and it will describe how that space will evolve over time based on some initial conditions. The equations only consider what is within the initial scale factor. Or at least that’s how I understand it.

I don't know where you're getting this from. Do you have a reference?

 

[rede96]

I don't know where you're getting that assumption about dark matter from. Nobody has a model in which dark matter is "an inherent property" of space, flat or otherwise. Dark matter is matter.

Sorry, that's a bit of a blunder. I meant dark energy of course. As in a type of geometry or even an infinite scalier field. But the point being it density doesn't change with expansion.

I don't know where you're getting this from. Do you have a reference?

Leonard Susskind's lectures on cosmology. I'll have to check my notes for which lecture, but I think's in the first one.

And this is not correct, as I've already said. A model with a finite amount of matter surrounded by emptiness out to infinity will not look, even in the observable part of it, like our observable universe actually does.

To be honest I've never seen or at least understood any proof that says there has to be an infinite amount of matter if space is infinite. So I am not disagreeing with you, just not aware of anything that states that fact.

But just for clarity, here it my thought process:

As I understand it, very simplified, there are just a few factors that effect how universe expands over time on larger scales. (From the FRW equations) Those being: Curvature, dark energy, matter & radiation density and initial conditions. Ignoring initial conditions and radiation density for simplicity, assuming space is flat and dark energy is a constant, that leaves gravity (matter density.) Oh and of course assuming the cosmological principle.

I think it's Newtons theorem that states if I want to know the gravitational effects on a distant object then I can encompass that object in a shell and only worry about the matter inside that shell as if all the mass was all at the center of the shell. Any mass on the outside of that shell can be ignored.

So that would suggest that I can arbitrarily chose any region of space, plug in the numbers and it would tell me how we'd expect that region to change over time. What happens outside the region, is for all intents and purposes irrelevant as I understand it. So I can assume that space can be infinitely big, dark energy is an infinite scalar field but the amount of matter is finite, ie. just what is inside my shell.

In essence that was pretty much how the FRW equation was derived wasn't it?

 

[PeterDonis]

I've never seen or at least understood any proof that says there has to be an infinite amount of matter if space is infinite.

There is no such proof and that's not what I was saying. There are certainly spacetimes that are spatially infinite but contain only a finite amount of matter--for example, any spacetime that describes an isolated gravitating mass surrounded by empty space. Physicists use such solutions to describe isolated systems all the time.

What I said was that no such solution describes the universe as a whole. See below.

I think it's Newtons theorem that states if I want to know the gravitational effects on a distant object then I can encompass that object in a shell and only worry about the matter inside that shell as if all the mass was all at the center of the shell. Any mass on the outside of that shell can be ignored.

This theorem (which is also valid in GR, btw) only says you can ignore matter outside the shell if the shell is spherical and if all of the matter outside the shell is spherically symmetric about the shell. Those conditions are valid for the universe as a whole if the universe as a whole is homogeneous and isotropic. But not otherwise. In particular, they are not valid for a shell centered on a point in a spacetime with a finite amount of matter surrounded by empty space, unless the chosen center point of the shell happens to be the exact center of the matter (and the matter is spherically symmetric). So we would have to be at the exact center of the universe, and moving exactly with the center of mass of the universe, for this model to be possible. But it is highly improbable that we are at the exact center, and even more improbable that we are motionless with respect to such a center, because we are moving relative to the CMB rest frame (i.e., the CMB has a dipole anisotropy as we see it), and the CMB rest frame would have to be the "center of mass" rest frame if the universe only contained a finite amount of matter (since the CMB rest frame is the frame in which the matter in the universe appears exactly spherically symmetric).

In essence that was pretty much how the FRW equation was derived wasn't it?

No. Susskind does use this as a heuristic argument for why the Friedmann equations are plausible, but the Friedmann equations are actually derived by solving the Einstein Field Equation for the case of homogeneous and isotropic matter. And the solutions that are derived that way do not include any that have a finite amount of matter surrounded by empty space.

 

[rede96]

What I said was that no such solution describes the universe as a whole. See below.

Ah ok. Thanks for the help on this. I did have a few more questions but they may be mute if I’ve understood you correctly.

So is it accurate to say that there is no model that would include infinite space and finite matter, which would both describe how our universe evolves as a whole and be consistent with GR?

 

[PeterDonis]

is it accurate to say that there is no model that would include infinite space and finite matter, which would both describe how our universe evolves as a whole and be consistent with GR?

To the best of my knowledge, yes, there is no such model.