The size of the universe confuses me.

[Surlethe]

So one can organize possible universes by local isometry?

[Kuroneko]

I'm not sure what you mean by 'organize', but though torus in some sense violates the 'spirit' of the physical isotropy condition (that you observe the same conditions in every direction)--for small torii, you will see a difference (e.g., in the ways images repeat across different, non-antipodal parts of the sky)--that doesn't really help you if the universe is many times that what you can observe.

[Surlethe]

Maybe I mean that "possible universes" is a category where the morphisms are local isometries.

I suppose that Occam's Razor would imply that, absent locally detectable effects of global topological properties, one should assume that the universe is one of the model geometries.

[Parricidium]

It's impossible for anything to move faster than light.

I only have an amateur understanding of it, but I'm fairly certain that is only partially true. Cherenkov radiation is when something passes through a medium faster than light does in said medium. So, while it doesn't go faster than the speed of light in a vacuum, particles can go faster than light in some mediums.

[Lord Zentei]

It's impossible for anything to move faster than light.

I only have an amateur understanding of it, but I'm fairly certain that is only partially true. Cherenkov radiation is when something passes through a medium faster than light does in said medium. So, while it doesn't go faster than the speed of light in a vacuum, particles can go faster than light in some mediums.

When talking about speed of light in this context, we're always understood to be talking about light in a vacuum.

[cosmicalstorm]

Here's a great paper on the multiverse theory written by Max Tegmark

Abstract: I survey physics theories involving parallel universes, which form a natural four-level hierarchy of multiverses allowing progressively reater diversity. Level I: A generic prediction of ination is an innite ergodic universe, which contains Hubble volumes realizing all initial conditions including an identical copy of you about 10^10^29m away. Level II: In chaotic ination, other thermalized regions may have dierent physical constants, dimensionality and particle content. Level III: In unitary quantum mechanics, other branches of the wavefunction add nothing qualitatively new, which is ironic given that this level has historically been the most controversial. Level IV: Other mathematical structures give dierent fundamental equations of physics. The key question is not whether parallel universes exist (Level I is the uncontroversial cosmological concordance model), but how many levels there are. I discuss how multiverse models can be falsied and argue that there is a severe \measure problem" that must be solved to make testable predictions at levels II-IV.

http://space.mit.edu/home/tegmark/multiverse.pdf