Can the Universe Transition from Finite to Infinite?

[Helios]

I want to get this simplest cosmology question asked once and for all because I don't get it. We have "cosmologicial models" which have the curvature of the universe going from positive to negative ( or maybe visa-versa ) at some stage ( or not? ). Now elsewhere we hear that a negatively curved universe is infinite and a positive one is finite. Now any student is going to ask "How can finitude become infinite?" ( or visa-versa? ) . Is what I've said flawed? Is there a contradiction? I am the amateur so the fault is surely mine. This must be a page one cosmology question with an elementary answer so can someone please explain? Someone can throw in some names of different universe shapes if they feel like it. Thanks.

edit--send to cosmology pls

 

[phinds]

In response to one part of your question, physical things that are finite cannot become infinite and things that are infinite cannot become finite. The universe either started out infinite or it started out finite. No one knows, but however it started out, that's how it is now. If it is finite, there is a very strong consensus that it is unbounded because a universe that is finite and bounded would have a center and an edge and our universe has neither.

 

[Helios]

No one is ever going to see "bounds" regardless of consensus. I did not mention bounds.

 

[PeterDonis]

We have "cosmologicial models" which have the curvature of the universe going from positive to negative ( or maybe visa-versa ) at some stage

Which models are you talking about? I'm not aware of any models where the sign of the spatial curvature of slices of constant time changes.

 

[Dale]

We have "cosmologicial models" which have the curvature of the universe going from positive to negative ( or maybe visa-versa ) at some stage ( or not? ).

This is not correct the way you are thinking of it. A better way to say this is that there are a family of models where some have positive and some have negative curvature.

This is related to the fact that conic sections are a family of figures which include ellipses (positive curvature, finite) and hyperbolas (negative curvature, infinite).

 

[PeterDonis]

A better way to say this is that there are a family of models where some have positive and some have negative curvature.

And in each model in the family, the sign of the curvature is fixed; it doesn't change from one spatial slice to another. (I know you know this, but I want to make sure the OP understands it.)

 

[Helios]

Thanks. It must be acceleration vrs deceleration that has the sign change. This
https://www.physicsforums.com/threads/accelerating-expansion-and-mediocrity-priniciple.850180/
confused me because I read
"when curvature is crossing from negative to positive"
and I misconstrued the meaning. I take it that flat or negative curvature is the most popular belief. Now are there multiple negative shapes or one, because I've heard "saddle" and also "trumpet or horn" as descriptive of negative curvature?

 

[PeterDonis]

I read
"when curvature is crossing from negative to positive"

The "curvature" referred to here is not spatial curvature; it refers to the curvature of the line on the graph describing our actual universe's deceleration/acceleration over time.

I take it that flat or negative curvature is the most popular belief.

Our best current model is that the universe is spatially flat.

are there multiple negative shapes or one

Multiple.

 

[Dale]

Now are there multiple negative shapes or one, because I've heard "saddle" and also "trumpet or horn" as descriptive of negative curvature?

There aren't really good words in English for the shapes of 4D pseudo Riemannian manifolds. I am not sure that any word will convey the geometry correctly, that is why we use math.

Saddle refers to the spatial shape and horn refers to the time evolution, so both are legitimate descriptions.