Infinite space in a finite bubble, in a Tegmark Level 2 multiverse?

[DanielJ2021]

TL;DR Summary

If our universe (in entirety, including all that lies beyond our observable universe), is spacially infinite[1], how can it exist alongside other infinitely large, and completely separate, universes in a Tegmark Lvl.2 multiverse (eternal inflation)?

[1]All evidence points to the universe being infinitely large, or so large that any curvature is potentially impossible to measure

So I am a layman in physics, I admit I am trying to grasp big ideas piecemeal via articles, wikipedia and YouTube. I don't pretend to be educated in this regard but I am curious and willing to learn!
The idea of the multiverse intrigues me. Sidestepping for a second the fact that the idea has been dismissed as basically religion for the fact that it is untestable for the time being, I just want to grasp the arguments around it.

Specifically for this thread my question is...in Tegmark's hierarchy of the multiverse, Level 2 represents the idea of eternal inflation breeding a multiverse. In this scenario a universe like ours might spawn randomly alongside an infinite number of others, each with different laws of physics. A universe like ours, and potentially all the rest, would be infinite in size. However, how can multiple infinitely-large universes co-exist in the multiverse? Where do they all fit?

Tegmark himself gives a clue but I would like clarity on this and up to date insight;
Surprisingly, it has been shown that inflation can produce an infinite Level I multiverse even in a bubble of finite spatial volume, thanks to an effect whereby the spatial directions of spacetime curve towards the (infinite) time direction (Bucher & Spergel 1999). (source attached)

Can someone talk me through this please? Thank you!

 

[mathman]

Multiverse and infinite universe are purely speculative. If you want them both just add more spatial dimensions.

 

[Bandersnatch]

Multiverse and infinite universe are purely speculative. If you want them both just add more spatial dimensions.

This is what the OP is talking about:
https://arxiv.org/pdf/0712.0571.pdf

 

[Bandersnatch]

I thought I'd bump this thread a bit, as I'd love somebody to take a crack at answering the OP.

I've never learned how to read the inflationary space-time diagrams, including how to interpret infinite spatial extent of the bubbles within the larger inflationary landscape, or in what sense are the bubble universes colliding.

I think the closest, tangentially-related answer I've managed to coax out of somebody (Peter, was it?), was that in de Sitter universes (such as during the inflation) the concept of spatial (in)finiteness is undefined, and one can only begin to talk about the spatial extent once there universe becomes radiation or matter dominated and the space-time can be sliced in a preferred fashion. Though I might be misremembering it altogether.
But the X-shaped space-time diagrams do show 'something', right? And the overlapping light-cones of each bubble have some physical meaning, right? Can these be mapped to some heuristics or analogies?

The entire thing remains mysterious. Any takers?