See: 9:36 to 23:00 – Amir challenges the assumption that space is infinite, by pointing out one of the traditional views whereby spacetime's 3D spatial existence (i.e., basically just space) didn’t exist until the universe itself emerged into existence via the so-called “big bang”.
Brian explains about the idea of pre-existing space, which supposedly extends via infinity, i.e., already exists without limit – the state of infinite existence.
See: 7:50 to 9:45 – Russell Stannard explains how space and time are fused together to form what we call “spacetime”, and describes the view whereby 3D space (i.e., simply spatial existence) as we experience it, is considered to be a projection from 4D spacetime (the block universe) itself – a relative projection based on events (physical matter; stuff) existing... in contrast to what would otherwise just be empty space.
The following linked page lists a video debate in which, Roger Penrose, Sean Carroll, and Laura Mersini-Houghton, each discuss their own ideas about multiple universes “Big Bang & Creation Myths” – produced by: “The Institute of Art and Ideas” ...
See: 14:56 to 17:10 – Roger Penrose emphasises that in accordance with relativity theory, distance has no physical meaning when only massless particles (e.g., photons) exist – length contraction (1st theorised via special relativity) is the subjective experience of space itself (not just matter) actually existing as being physically shorter, which varies according to how fast a given body is travelling through space relative to empty space and/or other physical bodies.
The following page lists a video which also explains: Roger Penrose's conformal cyclic cosmology, produced by: “PBS Space Time” – it includes a very nice visual illustration.
Related point: see Jack Fraser’s post: Photons don’t experience space – “Photons travel along null geodesics through spacetime”
If spacetime is considered to extend to infinity independent (pre-exists) of whether or not matter exists, then that seems to suggest an absolute length of space itself – i.e., equivalent to a reference frame of being at absolute rest in the universe (i.e., relative to the CMB; there must be a potentially slowest clock speed), but even when massive stuff does not exist – distance as normal, but nothing to experience it.
Point 1: Consider in what sense space itself might exist in Roger Penrose’s theory of “conformal cyclic cosmology” when only massless energy exists, compared to the obvious non-existence of space at the start of the traditional big bang idea, whereby physical matter, time, and space itself, first started to emerge?
Point 2: If space does not have an absolute existence (infinite or not) independent of whether massive stuff exists, then the very beginning of the traditional big bang would be very similar (i.e., same physics) to the exact moment that the very last massive particle becomes massless in Roger’s theory (according to Roger) – both scenarios would mean that distance has no meaning (effectively doesn't exist).
Two relevant points are below:
According to cosmologists, the so-called “traditional” big bang theory doesn't describe the very first moments.
The big bang smooth pop via “conformal cyclic cosmology” is probably supposed to happen sometime before the last massive particle becomes massless.
Big Point 3: It is impossible for straight-line distance to be infinite (see: “Straight-line distance infinity analysis”). Therefore, it seems rather strange when considering the totality of space (which exists at some finite unknown size), right now, but independent of massive stuff existing – it seems to suggest that matter could one day hit the edge of space – but what then? – Would matter become squashed by its own momentum? – Would space stretch to become larger than its pre-existing finite size?
Consider: can spatial existence actually exist when no massive particles exist? – Are space and physical matter metaphysically intertwined?