I got this in my mail box since I commented here ... oh, so long ago. A quick update is that singularities and inflation have been discussed.Irrelevant nitpicking first: Drakkit and phinds claim that singularities would give us no information. This is a fact in physics (signaling theory breakdown), but not in mathematics. (If memory serves, some singularities are sufficiently well behaved to give you one bit of information.)Maybe more interesting: rootone, phinds and Chronos claim that inflation is a hypothesis that is considered most likely to explain the evidence. More precise I hope is that the current standard cosmology, as given by the Planck archive papers, include an inflation like era (that would be the general theory part) and that an inflation field (that would be the specific hypothesis part) has passed a handful of tests but not one outstanding of resulting in - hopefully observable in the cosmic background radiation - primordial gravitational waves. It is hard to know from the literature, but Simon Foundation's Quanta site has described inflation as most popular theory and winning terrain despite the outstanding test. (Maybe those opposed fall aside from age, that is not unheard of?) Chronos claims that it would foster the notion that the universe must be finite, but I do not understand how as it is not an implication (rather the opposite I think, since eternal inflation seems to be a natural ground state of the quantum field) and the opposite hypothesis of an infinite universe is ever more spoken of. Maybe Chronos is thinking of the local out-of-inflation universe?So to the current question of how space expands. Maybe the confusion stems from conflating units with scaling? Cosmologist Susskind has several video series of lectures on the Stanford University site. As I remember it, he describes how cosmologists use a unit-less scale factor to describe increasing (as it were) or decreasing cosmological volumes in relation to unit-full coordinate points of (sufficiently gravitationally unbound) galaxy clusters. At one point in one series he deliberately describes how expansion would in principle insert more “standard unit” separated coordinate points as expansion proceeds.That would describe the involved equations I think, and map to the descriptions of volume increase (or coordinate point insertion). But it would not tell us much on what space is. Adding special relativity would tell us how space and time is related by light cone physics defined by the universal speed limit. And adding general relativity and thermodynamics would tell us that tilting those light cones into closed time-like curves does not seem to make sense, telling us either thermodynamics or general relativity is incomplete (and we already know the latter is). Space of general relativity, already a somewhat unfamiliar system, is not easily grokked it seems to me (who as already noted up thread has never studied it), and that is before we insert it into cosmology and gets the addition of universal quantum fields of the vacuum at various eras ...
