The BAO ruler is supposed to be rigid. The sound horizon frozen at the drag epoch stamps one comoving length into the galaxy distribution, and after reconstruction and standard nonlinear corrections, its measured position should not care whether the galaxy pairs being correlated sit in overdense superclusters or underdense voids (Eisenstein et al. 2007; Seo and Eisenstein 2007). Environment independence is what makes the ruler a ruler.
Density-split and environment-split analyses keep finding flex. The BAO peak appears compressed in overdense regions and stretched in underdense ones at the percent level or more (Roukema et al. 2015; Neyrinck et al. 2018), beyond what the standard accounting of nonlinear evolution, bias, and reconstruction comfortably explains. Within ΛCDM the shift is doubly awkward: the early-universe scale itself cannot vary, so any environmental dependence must be manufactured entirely by late-time nonlinear physics, and the model's machinery for that, perturbative mode-coupling plus reconstruction, is precisely the part that was supposed to have removed it.
The standing is an open modeling argument with real cosmological stakes, because environment-split BAO is graduating from curiosity to precision tool. DESI Year 5 and Euclid will measure the void-versus-cluster BAO position split at the tenth-of-a-percent level across multiple redshift bins, which is exactly the regime where a genuine environmental signal separates cleanly from nonlinear residuals.