What is the universe expanding into ? Eternal inflation

[windy miller]

Normally when one is asked what is the universe expanding into, the answer is its not expanding into anything. Space itself can expand. However In the context of eternal inflation, our universe is a bubble in a sea of inflating space. And hence assuming eternal inflation is right, does the standard answer need revising? Should one say that its expanding into the inflating space?

 

[Bandersnatch]

I don't see why it would need changing. Within the landscape of the eternal inflation, our universe is just a patch of space experiencing slower expansion than its surroundings.

The problem with saying something like 'expanding into inflating space' is that it implies that one patch of space somehow encroaches onto another - that a point in non-inflating patch can be carried by the 'regular' expansion into the inflating patch.
Whether points in the whole eternally inflating universe are within or without a non-inflating patch doesn't change them being comoving with whatever expansion is locally occurring. They can not be made to move past one another by expansion.