Why do we care how many universes there are and how they’re arranged?

1. We want to know!
2. It would be amazing if there were multiple universes.
3. The soft anthropic principle is most satisfying if there are many universes with different properties.

Possibilities

One and Done

It started with the Big Bang, and will end either with the Big Crunch or by drifting larger forever. The important thing is there’s just one.

Oscillating

Each universe starts with a big bang and ends with a big crunch, which recycles to the next universe. It could have different properties each time. Time is probably infinite in both directions – this never started and will never end.

This could result in an infinite number of universes over an infinite time. However, as soon as one universe has the property of expanding forever, instead of collapsing, it’s all over – that would be the last universe. Of course if time stretches back infinitely, there would still have been an infinite number of them til then (albeit a one-sided infinity, what’s that called?). Things would be real boring for the rest of infinity. Unless an expanding forever universe has a way of generating new universes, such as nested universes, below.

When my son, Caleb, was in jr hi, he pointed out that with time stretching back infinitely, all possible universes would already have existed! So if all infinities were the same size this would be true. But infinities comes in different sizes> – easiest to visualize is that although infinity x a zillion isn’t any bigger (where a zillion is any finite number),  infinity x infinity is bigger than the original. So if time is infinity long, but the number of ways a universe can be is infinity x infinity (and it might be even bigger, like infinity ^ a zillion), then all possible universes will never exist, no matter how long time lasts.

Multiverse

The Big Bang generated a bunch of universes; after the first brief moment they’re no longer in touch with each other. Physics identifies this with the faster-than-light expansion called Cosmic Inflation, after which different regions of the original universe can no longer communicate, so they’re effectively separate universes. They would probably have similar but not necessarily identical properties. Their lifespans would probably be independent. It’s hard to know if the above choices would apply to them independently or to the whole collection.

Multiverses

Our Big Bang could be local: it created our universe or multiverses, but there could be other big bangs or oscillating or whatever universes out there unrelated to our Big Bang. If so they probably have wildly different properties from our own local collection of multiverses.

Nested Universes

Fundamental particles in our universe would be whole universes, and our universe would be a fundamental particle one level up. This is my favorite option.

Seems like there are more possibilities in my notes. And these ideas are hardly original – I’ve probably encountered them all somewhere.