He doesn't say it's a new universe, e.g. in an interview with Lex Fridman[1] he calls that out and says it explicitly isn't a separate parallel universe. It's more an argument that if you don't have mass because all the mass has decayed, through Einstein's relation of mass and energy and Planck's relation of energy and frequency, and frequency involving distance and time, with no mass, you lose notions of distance and time. Then the infinitly large distant future universe and the infinitely small distant past big bang become indistinguishable with the loss of "large" and "small" to distinguish them. They are both "at infinity", they both "contain" all the energy in the universe, and what we see as a tiny big bang, aliens on the other side saw as a huge expanded universe.
From what I (layperson) can tell, it's like the expand/crunch cyclic universe theory, but without the need to crunch back down again.
What I get from this, and I might be totally misunderstanding, is that we can see it loosely as "zooming out" (or the sake of simplicity) with each iteration, until you're looking at a tiny universe again? So that large vs. small is just a matter of viewpoint.
I'm not sure how to interprete it in that sense, or what the math looks like, I have only Roger Penrose saying "the math checks out" to go on.
Sounds like you're asking "is it really getting bigger endlessly and we take a larger distance as the unit value each cycle" and if so, that feels like the wrong kind of question when talking about distance not existing, but I don't know anything deep about it I've only heard him talk about it in interviews.
I don't really get why you can't reason the other way and say if there are photons and light, then there must be frequency, distance and time, therefore energy, and therefore mass. Heck, maybe that is the same reasoning; there, at the place of infinity, is all the energy and mass which ever was in the universe, all in one place. And what do you get when the whole universe is all in one place? A big bang? Transforming from matter to light (via stars burning and eventually Hawking radiation from the last things remaining: black holes) carries all the energy in the universe off into the distance. Where does it go? Off into infinity. If you take infinity as a place that means it all goes to the same place? Then that process is the "collapse" which brings everything together into the same place ready to be turned into matter again? That's my pop-science understanding of his proposal.
From what I (layperson) can tell, it's like the expand/crunch cyclic universe theory, but without the need to crunch back down again.
[1] https://www.youtube.com/watch?v=orMtwOz6Db0