A New Probe of the High-z BAO scale: BAO tomography With CMB $\times$ LIM-Nulling Convergence

Standard rulers such as the baryon acoustic oscillation (BAO) scale serve as workhorses for precision tests of cosmology, enabling distance measurements that probe the geometry and expansion history of our Universe. Aside from BAO measurements from the cosmic microwave background (CMB), most standard ruler techniques operate at relatively low redshifts and depend on biased tracers of the matter density field. In a companion paper, we explored the scientific reach of nulling estimators, where CMB lensing convergence maps are cross-correlated with linear combinations of similar maps from line intensity mapping (LIM) to precisely null out the low-redshift contributions to CMB lensing. We showed that nulling estimators can be used to constrain the high redshift matter power spectrum and showed that this spectrum exhibits discernible BAO features. Here we propose using these features as a standard ruler at high redshifts that does not rely on biased tracers. Forecasting such a measurement at $z \sim 5$, we find that next-generation instruments will be able to constrain the BAO scale to percent-level precision at $7.2 \%$, while our futuristic observing scenario can constrain the BAO scale to $4\%$ precision. This constitutes a fundamentally new kind of BAO measurement during early epochs in our cosmic history.