When we talk about the Robertson-Walker scale factor in the early universe or the matter inside a black hole event horizon, there must be an arbitrarily large or infinite density.
But how can this be possible if we consider Fermi-Dirac statistics? I mean suppose the scale factor decreases toward early times. Can we squeeze the matter as much as the degeneracy pressure allows us in order to put a large amount of matter inside a limited physical space? How can we imagine a typical galaxy inside a smaller space that is not expanded as much as today, let alone all the galaxies in the universe? The same is true about a black hole. How can we explain infinite density and growing matter inside a limited physical space? Even if we say that their momentum quantum states are respecting the statistics but again there are particles which occupy physical space, which is by assumption far smaller than the current epoch or outside of a black hole event horizon.