Space/time curvature of the young universe?

[EskWIRED]

All over the news we see the results of the recent detection of gravity waves from the early universe.

Which got me wondering: The early universe was much more dense than at the present. It therefore seems that spacetime was much more curved than it is, on average, today.

Is this increased curvature apparent from studies of the CMBR? Is there any need to correct for it in calculations? Is it visually apparent when studying objects formed shortly after the big bang? Is it detectable in any manner?

 

[bcrowell]

Spacetime curvature is how gravity is described in GR. If you take the word "curvature" in your OP and replace it everywhere with "gravity," it basically doesn't change the meaning.

The Einstein field equations relate a certain measure of curvature (the Einstein tensor) to a measure of the mass-energy-momentum content of spacetime (the stress-energy tensor). The CMBR is the afterglow of a certain epoch after the big bang, so it directly shows us that there was matter, and it had energy. This connects directly to the curvature.

 

[craigi]

Spacetime curvature is how gravity is described in GR. If you take the word "curvature" in your OP and replace it everywhere with "gravity," it basically doesn't change the meaning.

The Einstein field equations relate a certain measure of curvature (the Einstein tensor) to a measure of the mass-energy-momentum content of spacetime (the stress-energy tensor). The CMBR is the afterglow of a certain epoch after the big bang, so it directly shows us that there was matter, and it had energy. This connects directly to the curvature.

Are we to conclude that if the universe is open or flat then it must've made a transition from closed? If so, what are the implications for matter distribution and the possibility of boundaries in the open and flat scenarios? If not, what is the mechanism that ensures that the universe maintains its shape throughout expansion?

 

[bcrowell]

Are we to conclude that if the universe is open or flat then it must've made a transition from closed?

No, that wouldn't be correct, and I don't see how it relates logically to my material that you quoted.

AIf not, what is the mechanism that ensures that the universe maintains its shape throughout expansion?

The Einstein field equations say that you can't have topology change unless there is exotic matter or closed timelike curves -- neither of which we think actually exists.

 

[craigi]

The Einstein field equations say that you can't have topology change unless there is exotic matter or closed timelike curves -- neither of which we think actually exists.

Am I right in thinking that this implies that if the density parameter is greater than 1 now, then it must have
been greater than 1 in the early universe and that if the density parameter is less than 1 now, then it must have been less than 1 in the early universe?

Does it also imply that if the universe is flat the the density parameter is and always has been exactly one? Or is a open-flat transition not considered a topology change?

If the universe is and always has been flat does that mean that new volume in the universe emerges at exactly the same rate as new "stuff" (eg. matter and dark energy)?

Is there any reason to believe that the density parameter is constant across all time?

Also, am I right to presume that when you say that we don't believe exotic matter to exist then you're not including dark matter in that?

Sorry for all these questions. I can't seem to find answers to them by just searching and they seem pretty important, at least to me.

 

[bcrowell]

Does it also imply that if the universe is flat the the density parameter is and always has been exactly one? Or is a open-flat transition not considered a topology change?

I see -- now I think I understand what you're getting at.

First off, keep in mind that spatial curvature is not the same thing as spacetime curvature. When we say that the universe is flat, we mean that its spatial curvature is zero, but its spacetime curvature is not.

Exact flatness requires that a physical parameter take on an exact value. In general, we don't expect that the evolution of any physical system will result, with any finite probability, in any parameter's attaining an exact value and retaining that exact value for any finite time interval. So I think it makes more sense physically to talk about an open-closed transition. That would definitely be a topology change.

Am I right in thinking that this implies that if the density parameter is greater than 1 now, then it must have
been greater than 1 in the early universe and that if the density parameter is less than 1 now, then it must have been less than 1 in the early universe?

Yes, that's right.

In general, the Friedmann equations predict that the universe will evolve away from flatness. This is the flatness problem: http://en.wikipedia.org/wiki/Flatness_problem The fact that the universe evolves away from flatness in realistic cosmological models is consistent with the more general theorem saying that we can't have topology change in GR (without exotic matter or CTCs). To get topology change, you would have to evolve *toward* flatness and then cross the line.

I don't know if it's true in general that the density parameter keeps a constant value over time. I suspect it's not true, but that it never evolves in the direction that would take you toward flatness. This kind of thing could get complicated in realistic cosmological models that include various matter fields.

If it seems spooky to you that the density parameter would maintain consistent behavior as it evolves over time, then consider the analogous Newtonian situation of a spherical shell of particles that explodes outward. Let's say that the cloud has exactly the minimum amount of energy needed to allow all the particules to escape to infinity, i.e., they're all moving at escape velocity. Then even as their density and kinetic energies change over time, any density parameter you define will always equal 1, simply because you define the density parameter by extrapolating the future evolution of the system.

 

[craigi]

Yes, that's right.

In general, the Friedmann equations predict that the universe will evolve away from flatness. This is the flatness problem: http://en.wikipedia.org/wiki/Flatness_problem The fact that the universe evolves away from flatness in realistic cosmological models is consistent with the more general theorem saying that we can't have topology change in GR (without exotic matter or CTCs). To get topology change, you would have to evolve *toward* flatness and then cross the line.

I don't know if it's true in general that the density parameter keeps a constant value over time. I suspect it's not true, but that it never evolves in the direction that would take you toward flatness. This kind of thing could get complicated in realistic cosmological models that include various matter fields.

If it seems spooky to you that the density parameter would maintain consistent behavior as it evolves over time, then consider the analogous Newtonian situation of a spherical shell of particles that explodes outward. Let's say that the cloud has exactly the minimum amount of energy needed to allow all the particules to escape to infinity, i.e., they're all moving at escape velocity. Then even as their density and kinetic energies change over time, any density parameter you define will always equal 1, simply because you define the density parameter by extrapolating the future evolution of the system.

I guess that there has been an effort to relate the maximum permissible fluctuation rate of the total relative density to the minimum bound of the flatness of the universe. It would be chaotic and even the tiniest fluctutation applied over 14 billion years would cause instability, right?

I'm also guessing that there have been research attempts to explain this by treating space and time as emergent properties related to energy and matter rather than fundamental dimensions that are curved by their presence.

Any idea where I would look for information on this?

 

[Chalnoth]

All over the news we see the results of the recent detection of gravity waves from the early universe.

Which got me wondering: The early universe was much more dense than at the present. It therefore seems that spacetime was much more curved than it is, on average, today.

Is this increased curvature apparent from studies of the CMBR? Is there any need to correct for it in calculations? Is it visually apparent when studying objects formed shortly after the big bang? Is it detectable in any manner?

The space-time curvature of our universe is manifested as the expansion of our universe. Yes, our early universe was expanding at a much higher rate than it is at present.