Where Is The Center Of The Big Bang Universe?

[sol invictus]

First, the universe is no longer flat, it is an open system, it is speeding up has of about 9 billion years ago.

That's incorrect. That fact that the expansion is currently accelerating is independent of the spatial geometry and does not constrain it in any way.

 

[Paulhoff]

That's incorrect. That fact that the expansion is currently accelerating is independent of the spatial geometry and does not constrain it in any way.

Did I say the word "constrain".

Paul

 

[sol invictus]

Did I say the word "constrain".

Did I say you did?

You said "the universe is no longer flat, it is an open system, it is speeding up has [sic] of about 9 billion years ago."

It is true that the expansion of the universe is accelerating, but it is probably false that the universe is open, and the existence of that acceleration does not tell us anything about whether the universe is flat, open, or closed.

 

[RecoveringYuppy]

Ever play a video game where, when you go off the edge of the screen, you wrap around and appear on the opposite side? That's a 2-torus - a 2D analogue of a 3-torus, and both a 2 and 3-torus are flat in the sense that they have zero spatial curvature. Put another way, unlike a flat map of the earth, there is no distortion or stretching when you represent the 2-torus in that video game using a flat screen.

I may be taking the video screen analogy too far.

In that analogy, when you walk off the top or bottom of the screen you can view the world as if that dimension is wrapped around a cylinder. Similarly when, walking off either side you can then view the world as being wrapped around a cylinder that is perpendicular to the other cylinder. Is that the geometry you are describing with the term 2-torus?

 

[Paulhoff]

Did I say you did?

You said "the universe is no longer flat, it is an open system, it is speeding up has [sic] of about 9 billion years ago."

It is true that the expansion of the universe is accelerating, but it is probably false that the universe is open, and the existence of that acceleration does not tell us anything about whether the universe is flat, open, or closed.

A closed system will slow stop and collapse, a flat system slows down with time but will never stops, the universe is speeding up and therefore is open.

Paul

 

[steenkh]

However (and this is not standard, but it's perfectly consistent) one can take the flat universe and "compactify" each of the three spatial directions independently. That gives you something called a 3-torus.

Ever play a video game where, when you go off the edge of the screen, you wrap around and appear on the opposite side? That's a 2-torus - a 2D analogue of a 3-torus, and both a 2 and 3-torus are flat in the sense that they have zero spatial curvature. Put another way, unlike a flat map of the earth, there is no distortion or stretching when you represent the 2-torus in that video game using a flat screen.

HMm, that was how I always imagined space before they found it was flat, but I was not aware that torus's could be flat. If that is true, it would solve all my objections, but it will also mean that if we travel indefinitely in one direction, we should end up where we came from, and as I remember, that was specifically what was denied in the first article I read about the flat universe.

 

[sol invictus]

In that analogy, when you walk off the top or bottom of the screen you can view the world as if that dimension is wrapped around a cylinder. Similarly when, walking off either side you can then view the world as being wrapped around a cylinder that is perpendicular to the other cylinder. Is that the geometry you are describing with the term 2-torus?

Yes.

Now try to picture a 3-torus . That's a possible flat but finite spatial geometry for the universe.

A closed system will slow stop and collapse, a flat system slows down with time but will never stops, the universe is speeding up and therefore is open.

You're wrong. Want me to show you the solutions to Einstein's equations to prove it?

 

[Paulhoff]

Yes.

Now try to picture a 3-torus . That's a possible flat but finite spatial geometry for the universe.



You're wrong. Want me to show you the solutions to Einstein's equations to prove it?

Oh, please do.

Paul

 

[steenkh]

A closed system will slow stop and collapse, a flat system slows down with time but will never stops, the universe is speeding up and therefore is open.

Right. But is "closed" the same as "finite" and "open" the same "infinite"? If the universe is infinite, there cannot be an average distribution of matter if there is not an infinite amount of matter.

 

[sol invictus]

Oh, please do.

OK, later today when I have a chance.

 

[sol invictus]

All right, very quickly:

[latex]$ds^2 = -dt^2+e^{2 Ht} (dx^2+dy^2+dz^2)$[/latex]

That's a solution to Einstein's equations with accelerating expansion, and it's flat.

[latex]$ds^2 = -dt^2+{\cosh^2 (Ht) \over H^2} d\Omega_3^2$[/latex]

That's a solution to Einstein's equations with accelerating expansion, and it's closed.

[latex]$ds^2 = -dt^2+{\sinh^2 (Ht) \over H^2} dH_3^2$[/latex]

That's a solution to Einstein's equations with accelerating expansion, and it's open.

The last two both accelerate at late times, and in fact are more and more indistinguishable from the first as t tends to infinity.