I stand corrected on these points. I have heard others like Sean Carroll say that it applies to classical space time. When I heard him say “classical” I thought he meant according to general relativity. But I went looking for more and this is what he meant by that:
The theorems in question make a simple and interesting point. Start with a classical spacetime — “classical” in the sense that it is a definite four-dimensional Lorentzian manifold, not necessarily one that obeys Einstein’s equation of general relativity. (It’s like saying “start with a path of a particle, but not necessarily one that obeys Newton’s Laws.”) The theorem says that such a spacetime, if it has been expanding sufficiently fast forever , must have a singularity in the past. That’s a good thing to know, if you’re thinking about what kinds of spacetimes there are.
My apologies for confusing the terms.
Also sorry for linking a video. I didn’t know what your rank was.