I do not think there is way to tell.
I'll refer to wiki;
The universe's size is unknown, and it may be infinite in extent.
[19] Some parts of the universe are too far away for the light emitted since the
Big Bang to have had enough time to reach Earth or space-based instruments, and therefore lie outside the observable universe. In the future, light from distant galaxies will have had more time to travel, so one might expect that additional regions will become observable. Regions distant from observers (such as us) are expanding away faster than the speed of light, at rates estimated by
Hubble's law.
[note 3] The
expansion rate appears to be accelerating, which
dark energy was proposed to explain.
But when placed on a torus-shaped universe , can the expansion rate not also naturally accelerate without the need for dark energy and without the light from outside the observable portion of the torus ever reaching us and observable lights actually disappearing beyond that horizon.
Using the fish analogy, a fishes universe is the pond, it was born there and will die there never knowing trees and clouds above.
That's a poor analogy . There are many fish that rise above the water surface and even fly through the air, and crawl on land.
An ant too, lives on a flat surface so thinks his world is only two dimensions, he cannot travel up and down.
Don't tell that to the herder ant. They herd aphids and strictly control where the aphids are to graze.
So to with us, the Universe is everything by definition so we cannot step out of it and see what shape it is.
OK, I agree, but can we examine the universe from the inside out and determine it's shape by observable geometrics?
I have not looked into it recently but from what I remember cosmologists are more interested in the exact value of Omega, regarding the density and expansion (plus DM dark energy etc but ill keep it simple)
Like I said it is looking flat w.r.t that number.
But Omega is not a measurements of flatness but of curvature, no? And is it not used to estimate the size of the universe?
Cosmologists also say the universe could be spatially infinite but temporally finite. That is a thinker.
Oh boy, you're not going to like this. IMO, outside the universe there is only a timeless, dimensionless condition and inside the universe time is an emergent property along with duration. The dimension of time emerges along with the duration of universal existence.
If the Universe were to have extant future that would argue for a torus shaped universe.
One misconception is that the universe began as a small, point in space and then expanded into that space.
Well, that is a relative statement, isn't it?
First, the expansion began from a region of space time as per above and it did not expand “into” anything, the space itself expanded and is still expanding.
I agree, there is no outside the universe but a timeless dimensionless condition. The universe is creating spacetime as it expands.
If the universe is finite now it always was.
I agree with that. It seems illogical to have an infinitely expanding universe with finite energy
The “observable” universe is parts we can see and that is restricted by the speed of light, if there is a region of the universe that is accelerating away from us faster than C,
And that does not rule out a toroid universe, alternately expanding and contracting from and to a central singularity
then the light will never reach us.
In a toroid universe any light that has passed the equator horizon would be invisible until our spacetime slice also passed the equator.
There are galaxies we can see now but will disappear as a result, over time all galaxies will have vanished with the exception of galaxies like Andromeda.
Is it possible that Andromeda is at the equator and has stopped receding while we are catching up towards the equator?
Could we measure if Andromeda and Milky Way are
accelerating towards each other?
Whether the universe is 3 sphere or whatever is a lot less interesting, to me at least.
Of course, you have a different relationship to science than I.
No, physics is the study of fundamental forces and mass in the universe from the very small the universe itself.
Obviously there are numbers involved but just quit sticking the word value in where ever you can, it's usually wrong.
I disagree. The universe cannot do anything with a force or a mass unless that force or mass has a deterministic value that determines the interactive result. 1 lb of mass + 1lb of mass = 2lb of mass regardless how you want to symbolize it in human terms.
Deterministic Inputs must exist of discrete amounts (deterministic values), in order to produce determined outputs with discrete result.
I don't see how that can be problematic.
The deterministic nature of natural processes demand discrete relational processing values, else you get garbage in, garbage out.