On the implications of the `cosmic calibration tension' beyond $H_0$ and the synergy between early- and late-time new physics

The cosmic calibration tension' is a $> 5σ$ discrepancy between the cosmological distance ladder built from baryonic acoustic oscillations (BAO) calibrated by the Planck/$Λ$CDM sound horizon ($r_s$) and Type Ia supernovae (SN1a) calibrated instead with the S$H_0$ES 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 $H_0$, and the implications for physics beyond $Λ$CDM. Of utmost importance, it implies a larger physical matter density $ω_m\equiv Ω_m h^2$, as both the fractional matter density $Ω_m$ and $h\equiv H_0/100$ km/s/Mpc are well constrained from late-time data. New physics in the pre-recombination era must thus be able to decrease $r_s$ while either reducing the value of $Ω_m$, or increasing the value of $ω_m$. Assuming a $Λ$CDM-like primordial power spectrum, this necessarily results in an increase in the clustering amplitude $σ_8$. Deviations from $Λ$CDM in the late-time expansion history cannot resolve the calibrator tension but can help relax the required shifts to the matter density and $σ_8$: 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 $ω_m$ 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.