Well, here we do not talk about knowledge that have no immediate application. We talk about knowledge that by definition (the unobservable beyond the universe) will never have application.
I vote for the observable universe to be named the falsifiable universe, the notion of the universe that experimental physicists inhabit in mind and body.
I've long regarded the unobservable universe as akin to an analytic continuation.
Analytic continuation often succeeds in defining further values of a function, for example in a new region where an infinite series representation in terms of which it is initially defined becomes divergent.
Far from being useless, these are tremendously useful in suggesting new ways to approach the mathematics of the original function.
So we have two things here: the falsifiable universe, and its intellectually stimulating analytic continuation.
If you're burning through chalk and pencils on an exponent growth curve, you'll soon give the analytic continuation some terse symbols, such as i and by the human psychology of oft-masterbated terse symbols, you'll come to regard it as being as real as any other symbol dripping down from the Matrix.
If you're lucky, at some point the unobservables all cancel out, and you're left with an insight into the falsifiable universe, arrived at through a mathematical worm hole. Mathematics folds in on itself in mysterious ways, no quantum particles required, so far as I've been able to tell.
The first requirement of a falsifiable universe is the state of being casually connected. If the falsification process is embedded in the falsifiable universe, there are additional requirements: you're dealing at least with a self-falsifiable universe. Falsification, it turns out, itself sits pretty far up the food chain.
Here's a good gig. Posit some primitive element amenable to nearly limitless analytic continuation, such that it can never be shown that there does not exist a continuation capable of collapsing back through some miracle of symbolic reduction to a testable statement about the falsifiable universe.
Congratulations. You have now made it permanently impossible to tell whether you're doing physics or not. It's important that the math is in some way highly constrained and very difficult, or it becomes immediately obvious that the playground exceeds the project.
If the constraints are difficult enough that you can tell the difference between the really smart people and the really, really smart people, and an Ed Witten or two comes along from time to time to humiliate the really, really smart people you've at least got the foundations in place for a credible intellectual discipline. If not physics, at least it's a sport.
It's just too bad that most of the people doing quantum-cosmic analytic continuation pass themselves off as physicists. Different rules, different discipline, whether or not they share the first twenty years of the same education. You can tell there's a lot of strain over this because the string people mutter the word "testable" as often as Microsoft mutters the word "innovation"—and to equal effect.
If we had a nice standard of elegance E and a proven theorem stating that all theories of physics more elegant than e are necessarily true, we could mend the house.
But we haven't yet written down the most surpassingly elegant equation that's actually false as witnessed in the falsifiable universe. Without an objective decision point, it's just a bunch of exceedingly smart guys refusing to kill their darlings.