It seems to me that "universe" and "exist" are defined cyclically. When not talking about many worlds or parallel universes, it's clear what it means to say whether or not a thing exists. All definitions are eventually cyclic, but this is something we intuitively understand and can point to real life examples of, eg.
Things that exist: My laptop, Clouds, Beluga whales, Post-lunch lethargy
Things that don't exist: Unicorns, Halting oracles (for a Turing-complete language), Perpetual motion machines
We have concrete evidence of things in the former list. The things in the latter list have well-defined and straightforward behavior and we know what evidence we might expect to see in the world if they existed, so it seems likely they don't. But this same intuition for determining whether or not a thing exists doesn't seem to apply when introducing "many worlds" into the discussion. By definition, things that "exist" in another universe don't impact our world in a way we can observe. So what does it mean to say that it "exists"?
Is there an alternate way to define "universe" and "exist" so that they're not circular?
Note 1: I'm referring to "parallel" universes such as those hypothesized under MWI; not fictional universes (eg. Marvel cinematic universe) which I have no difficulty with the definition of.
Note 2 (Only read this if it's unclear to you what an answer to this question might look like; the following is a "false" answer; something that has approximately the right structure, but fails to hold up under further scrutiny):
Structure of an answer: This is a solution I thought of that sounds right initially, but doesn't quite work (and I'll explain why it doesn't work at the end), but perhaps it serves as a good template for the sort of answer I'm looking for:
Alice and Bob are friends who live on the edge of each other's cosmological event horizon and have been chatting for the last couple million years. Alice's subjective experience has been that each time she sends a message to Bob, it takes significantly longer to get his response than it did last time. But Bob's experience mirrors Alice's. It's taking longer for her responses to reach him as well. Their experiences are symmetrical and each can compute the date at which they will no longer be able to communicate and even chat about their experience of losing touch forever but neither one anticipates ceasing to exist.
Now let's imagine that decoherence (the process under MWI by which Everett branches cease to be able to interact with each other) is a gradual process rather than an instantaneous one. Even if this is false, it's necessarily true for large complex structures like people built out of many atoms. Alice has been chatting with her Everett clone who's switched gender identities and taken to calling himself Bob. That is, Alice and Bob are composed of different quantum states of the same molecules and they are interfering with each other because particles do that sometimes. As Bob is fading from existence, Alice says to him, "Oh no! You're fading away!"
Under MWI, we might expect Bob to say "Well it looks to me like you're fading away!". Their experiences are symmetrical just as they were in the cosmological event horizon example. Neither views themselves as being in the process of disappearing. They're just losing track of each other.
Conversely, in a one-universe model, Bob might notice himself fading from existence (like Marty at the "Enchantment Under the Sea" dance in Back to the Future).
Initially, this feels like an answer to me, but the problem is that I don't think anyone subscribes to what I claimed above was the MWI model. Bob behaves as if he's still interacting with his universe and it's still solid. Suppose Bob's hands have faded away in Alice's universe. So Alice can no longer interact with Bob's hands. She asks Bob to clap his hands and tell her if they make noise. He claps his hands and claims that they do make a noise (because that's what he's experiencing). This means that the molecules in his hands, while no longer directly affecting Alice's universe by bouncing light into her retinas, are still indirectly affecting Alice's universe by sending pressure waves to Bob's ears, transforming into electrical signals in his brain, and then causing him to speak words which become pressure waves that reach Alice's ears and then become electrical signals in her brain.
But decoherence isn't about things becoming "invisible" in that they impart some effects on your universe but not others, it's about things ceasing to impact your universe in any way whatsoever.