Before we move on to what we don’t know about [cosmological] inflation, there are a few things we do know that are worth mentioning.
1. Inflation isn’t like a ball — which is a classical field — but is rather like a wave that spreads out over time, like a quantum field.
2. This means that, as time goes on and more-and-more space gets created due to inflation, certain regions, probabilistically, are going to be more likely to see inflation come to an end, while others will be more likely to see inflation continue.
3. The regions where inflation ends will give rise to a Big Bang and a Universe like ours, while the regions where it doesn’t will continue to inflate for longer.
4. As time goes on, because of the dynamics of expansion, no two regions where inflation ends will ever interact or collide; the regions where inflation doesn’t end will expand between them, pushing them apart.
(This only gets us to Tegmark Level 1.)
Some exorbitant multiverse complications:
[Paul] Davies argued that in a multiverse, “‘fake universes’ would be even more likely to vastly outnumber real universes [than in our one universe without a multiverse], so that if we live in multiverse, we would be overwhelmingly more likely to be living in a simulated reality. But that would imply that the laws of physics in our universe are also overwhelmingly more likely to be simulations and therefore cannot be used to conclude that there is a multiverse! So there is an inconsistency at the heart of the multiverse concept.”
Let’s unpack the argument and lay it out. To Davies, “If you take seriously the possibility of a multiverse of all possible universes, including all possible variations, then there would have to be at least some of those universes where sentient civilizations would advance to the point where they would have sufficient computing power to simulate entire fake worlds (like in the ‘Matrix’ movies). Simulated universes are much cheaper to make than the real thing. So once you’ve got civilizations throughout the multiverse that can simulate universes,” Davies stressed, then this is what they will do, and do increasingly.
As a result, “the number of fake universes in a multiverse will proliferate greatly and very soon outnumber real ones.” [Is Our Universe a Fake?]
Fake universes, Davies said, “undermine all the arguments for a multiverse,” because arguments for a multiverse are based on the physics of this universe. “But if ours is a simulated universe, then our laws are simulated, too, which means that the whole of physics is a fake.” And if the whole of physics is a fake, Davies said, then the whole argument for a multiverse collapses. The reason is that while the multiverse argument proceeds from the physics humans have discovered in this universe, people cannot use this argument because it then leads, surprisingly, to the conclusion that this is a fake universe, with fake physics.