Universe: Infinite Nature & Finite Singularity

[Jenny]

Many books say "this model of the universe is infinite in nature"
Say the Standard Big Bang Model can be infinite in nature if it has hyperbolic/ flat space.
My questions are:

1. how can an infinite universe begin with a finite singularity?

2. a universe with spherical geometry is finite in space but has no edge because it comes back on itself.
(analogy being the spherical Earth with no edge- analogy is dodgy because Earth exists in 3-D space where as we shouldn't view our universe as existing in a higher dimension)
What does edgeless mean in an infinite universe? I guess my question is- what characterises/ quantify/ qualify an infinite universe?
(eg. is it the maths?)

 

[VikingF]

1. how can an infinite universe begin with a finite singularity?

I asked about the exact same in another thread here:
https://www.physicsforums.com/showthread.php?t=125843&page=2

2. a universe with spherical geometry is finite in space but has no edge because it comes back on itself.
(analogy being the spherical Earth with no edge- analogy is dodgy because Earth exists in 3-D space where as we shouldn't view our universe as existing in a higher dimension)
What does edgeless mean in an infinite universe? I guess my question is- what characterises/ quantify/ qualify an infinite universe?
(eg. is it the maths?)

What do you really mean by this? If the universe is infinite, it has no limits by definition. If you go x lightyears in one direction (without turning around), you will never come back to the starting point, which actually is the case in a closed (finite) universe.

Maybe I misunderstood this question...?

 

[marcus]

Many books say "this model of the universe is infinite in nature"
Say the Standard Big Bang Model can be infinite in nature if it has hyperbolic/ flat space.
My questions are:

1. how can an infinite universe begin with a finite singularity?

I think the answer to your question #1 is: IT CAN'T.
I don't know of any book that says the initial singularity has to be spatially finite.
Nobody I know of assumes it has to be spatially finite (unless the universe is spatially finite).
Maybe some popular science book describes the initial singularity in intuitive language which gives readers the impression that it has to be bounded, or even confined to a single point.

A singularity is a (possibly infinite) region where a theory fails----i.e. fails to compute, gives meaningless answers, like infinite curvature (!) infinite density (!) etc.
(You are right to suppose that a spatially infinite universe cannot arise from a spatially finite singularity, but this is technically not a problem, since nobody pretends that it can.)

2. a universe with spherical geometry is finite in space but has no edge because it comes back on itself.
(analogy being the spherical Earth with no edge- analogy is dodgy because Earth exists in 3-D space where as we shouldn't view our universe as existing in a higher dimension)
What does edgeless mean in an infinite universe? I guess my question is- what [describes] an infinite universe?
(eg. is it the maths?)

YES IT IS THE MATHS because that is what cosmology is. Cosmology deals with math descriptions of universes.

Moreover the basic math needed is not very hard.
I guess you have heard of R² the mathematical ideal picture of an infinite flat sheet of graph paper.
Probably you also know of R³ the mathematical idea of an infinite 3D "graph paper".

these things are edgeless, if you study them by themselves, no surrounded by any higher dimensional space.

Also there is R⁴ the mathematical picture of infinite 4D graph paper.

It is extremely edgeless.

It does not take a lot of fancy math to begin studying these things. One can define distances, and angles, and areas and or volumes, etc. and continuous paths etc.

So the beginning is easy and straightforward, and you may have been thru all that, but it does not necessarily stop there.

all these things are examples of differentiable manifolds and there are other examples. they aren't necessarily all flat. the curvature of one of them can be defined INTERNALLY by some clever surveying tricks without ever having to suppose any surrounding space. So you can have a BUMPY infinite space.

the kind of mathematics that describes finite and infinite differentiable manifolds, using internal surveying methods, is called DIFFERENTIAL GEOMETRY-----it isn't hard. college sophomores or juniors take it, after a good course in calculus.

to repeat your second question

I guess my question is- what [describes] an infinite universe?

the answer is that what describes it is the techniques you learn in differential geometry.
(a lot of it is so intuitive that you can almost give verbal analogies and nontechnical equivalents---but it is still safer to back it up with math definitions, if you do that sort of thing)