On the implications of the `cosmic calibration tension' beyond H₀ and the synergy between early- and late-time new physics

The `cosmic calibration tension' is a > 5 discrepancy between the cosmological distance ladder built from baryonic acoustic oscillations (BAO) calibrated by the Planck/CDM sound horizon (rₛ) and Type Ia supernovae (SN1a) calibrated instead with the SH₀ES absolute magnitude, assuming the distance-duality relationship (DDR) holds. In this work, we emphasize the consequences of this tension beyond the value of the Hubble constant H₀, and the implications for physics beyond CDM. Of utmost importance, it implies a larger physical matter density ₘ ₘ h², as both the fractional matter density ₘ and h H₀/100 km/s/Mpc are well constrained from late-time data. New physics in the pre-recombination era must thus be able to decrease rₛ while either reducing the value of ₘ, or increasing the value of ₘ. Assuming a CDM-like primordial power spectrum, this necessarily results in an increase in the clustering amplitude ₈. Deviations from CDM in the late-time expansion history cannot resolve the calibrator tension but can help relax the required shifts to the matter density and ₈: it is in that sense that a combination of early and late-time new physics may help alleviate the tension. More precisely, models that modify the pre-recombination expansion history can accommodate the increase in ₘ without the need for additional modifications. It is those models which only affect recombination that require additional deviations at late-times to be successful. Hence, the `cosmic calibration tension' points either to a targeted modification of the pre-recombination expansion history, or to a broader change affecting multiple cosmic epochs.