One thing to bear in mind is that while the papers tend to just elide over it with some references, and the popsci representations of these discussions tend to

One thing to bear in mind is that while the papers tend to just elide over it with some references, and the popsci representations of these discussions tend to skip over this either because they don't think anyone else will understand it, or the authors don't understand it themselves, is that there are assumptions built into these declarations, and it can help to dig into them. It's not a bad thing that there are assumptions; they're entirely necessary to make the questions something amenable to serious analysis, since the infinite space of all possible physics isn't really something we can speak about intelligently except in some really limited ways. But you do want to keep that in mind as you read these things. Generally some physics are carried over from the real universe, and you want to look at how much. For instance, in this case, we carry over a very general-relativity-inspired gravity, which is then modified anyhow since GR-gravity wouldn't work. I've also seen another paper which was based on the premise "Assuming the basics of string physics are correct and we only vary the number of spatial and temporal dimensions, is life possible?" It's an interesting question, but "assuming the basics of string physics" is a big beginning. It doesn't invalidate the results, you just have to consider the results in the context of that. The objection to 4-space is that you can't have any stable orbits with an inverse-cube law of gravitation. As for the natural question "why can't we just assume inverse square gravity then, if we're trying to build a universe where life could exist?", and the answer is, you can! But you make it very hard on yourself to write a sensible, published paper in the process, because you've taken a huge step away from all known gravity theories and you're now on your own. I've often mentally noodled around with the idea of a two-dimensional universe based on a cellular automata theory, but in which one of the things the cells can do is be split in half (or quarters) somehow, with some defined mechanism for interacting with the original outer cells, and then the ability to further recursively split inside, and where the clock ticks, say, twice as fast in the split cells, so you end up with a universe that is (presumably) Turing complete, and participants may end up with the ability to perform infinite computations in finite time due to the split mechanisms. Presumably, if something like this could be defined, some sort of life could run in it; it seems to me than any Turing-complete (suitably modified with our often-also-elided assumptions about being finite-but-large-enough to act more like a Turing machine and less like a state machine, even if it is finite) environment can support life, on some level or other, even if by simulating some other more congenial environment. And the space of "physics" that permits Turing machines strikes me as very, very large compared to the space of "physics" that is "like ours, but just slightly tweaked". But you can't really get a math-heavy physics paper out of that idea.