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.)