Abstract
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 $r_s$. Assumption of
the $Łambda$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 $Łambda$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 $r_s$ in the $Łambda$CDM model extended to allow
additional light degrees of freedom.
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