The math also calls into question the Copernican principle — the idea that the Earth’s location does not occupy a special place in the universe.

“Both the Lambda-cold dark matter model and a spherically symmetric spacetime produce a special place where we must lie for the model to be physically plausible,” Temple said. “If this principle rules out one, it has to rule out the other.”

the list of people who have questioned them before includes vera rubin, who basically destroyed her career to do so (rubin-ford effect, which is still largely accepted as averaging out over larger distance scales for the particular voids she included in her study. i believe she had the right question with the wrong dataset). now that it's been fifty years it's not so much a career-killing question, since we have in the intervening time run through most of the other options and come up with nothing

discarding these axioms does in fact put the earth in a "special place" in a limited sense (density or other features may vary over large distances; one end of the observable universe may be distinct from the other), but not in like, a precopernican geocentric cosmology. we are in a special area, that's kind of a given (on a filament and not in a void; in the "green valley" and not in a highly star-producing nor a dead galaxy ...), what anisotropy and nonhomogeneity call into question is whether these features tend to average out over extremely large distances

more technically, what the paper does is apply range constraints to identify a ("maximal asymptotically stable") cluster of solutions of FLRW models that allow an amount of underdense radial perturbation without the use of expansion. this is an appeal to mathematical stability, in relation to a longstanding question in cosmology (why do these laws seem to be impossibly balanced?)