That's where interpretations come in. What is the physical relationship between nature and the wave function? Nobody knows. But interpretations guess and postulate .
Yes, the idea that there is a point beyond which we cannot see is unfalsifiable, because no matter how far one looked, one could always claim that one simply hadn't looked far enough. (It is worth noting that this is the starting point of Bayesian reasoning, which underlies much of modern science. It is the minimum assumption. The maximum assumption would be that everything known now is the extent of all that exists.) However, the cosmological considerations are about something else. It is observed that the universe is expanding . Our cosmological model to explain this is based on General Relativity with a positive cosmological constant .
And if we assume General Relativity is correct (we don't have to, but nobody has found anything better ), one of its predictions is a Cosmological Horizon at a particular place with respect to any point in the universe. This isn't testable, but it's a prediction of a testable theory (General Relativity) and that theory is the simplest, most successful we have in fundamental physics.
You're just describing a wave function as a multiverse . The measurement problem remains unsolved, and therefore nobody can observe a wave function. Call that inner product of vectors in a Hilbert Space a multiverse if you will, but I don't think we can call it anything until we have a solution to the measurement problem.
That's where interpretations come in. What is the physical relationship between nature and the wave function? Nobody knows. But interpretations guess and postulate .
Yes, the idea that there is a point beyond which we cannot see is unfalsifiable, because no matter how far one looked, one could always claim that one simply hadn't looked far enough. (It is worth noting that this is the starting point of Bayesian reasoning, which underlies much of modern science. It is the minimum assumption. The maximum assumption would be that everything known now is the extent of all that exists.) However, the cosmological considerations are about something else. It is observed that the universe is expanding . Our cosmological model to explain this is based on General Relativity with a positive cosmological constant .
And if we assume General Relativity is correct (we don't have to, but nobody has found anything better ), one of its predictions is a Cosmological Horizon at a particular place with respect to any point in the universe. This isn't testable, but it's a prediction of a testable theory (General Relativity) and that theory is the simplest, most successful we have in fundamental physics.