Résumé
The `cosmic calibration tension' is a$> 5\sigma$discrepancy between the cosmological distance ladder built from baryonic acoustic oscillations (BAO) calibrated by the Planck/ $\Lambda$ 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$\Lambda$ CDM. Of utmost importance, it implies a larger physical matter density$\omega_m\equiv \Omega_m h^2$ , as both the fractional matter density$\Omega_m$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$\Omega_m$ , or increasing the value of$\omega_m$ . Assuming a$\Lambda$ CDM-like primordial power spectrum, this necessarily results in an increase in the clustering amplitude$\sigma_8$ . Deviations from$\Lambda$ CDM in the late-time expansion history cannot resolve the calibrator tension but can help relax the required shifts to the matter density and$\sigma_8$ : 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$\omega_m$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.