Sounds Discordant: Classical Distance Ladder & $\Lambda$CDM -based Determinations of the Cosmological Sound Horizon

Type Ia Supernovae, calibrated by classical distance ladder methods, can be used, in conjunction with galaxy survey two-point correlation functions, to empirically determine the size of the sound horizon $r_{\rm s}$. Assumption of the $\Lambda$CDM model, together with data to constrain its parameters, can also be used to determine the size of the sound horizon. Using a variety of cosmic microwave background (CMB) datasets to constrain $\Lambda$CDM parameters, we find the model-based sound horizon to be larger than the empirically-determined one with a statistical significance of between 2 and 3$\sigma$, depending on the dataset. If reconciliation requires a change to the cosmological model, we argue that change is likely to be important in the two decades of scale factor evolution prior to recombination. Future CMB observations will therefore likely be able to test any such adjustments; e.g., a third generation CMB survey like SPT-3G can achieve a three-fold improvement in the constraints on $r_{\rm s}$ in the $\Lambda$CDM model extended to allow additional light degrees of freedom.