A new method to build the (inverse) distance ladder

The cosmic distance ladder is the succession of techniques by which it is possible to determine distances to astronomical objects. Here, we present a new method to build the cosmic distance ladder, going from local astrophysical measurements to the CMB. Instead of relying on high-redshift cosmography in order to model the luminosity-distance relation and calibrate supernovae with BAO, we exploit directly the distance-duality relation $d_L = (1+z)^2 d_A$---valid if photon number is conserved and gravity is described by a metric theory. The advantage is that the results will not depend on the parametrization of the luminosity-distance relation at $z>0.15$: no model is adopted in order to calibrate BAO with supernovae. This method yields local measurements of the Hubble constant and deceleration parameter. Furthermore, it can directly assess the impact of BAO observations on the strong 4--5$\sigma$ tension between local and global $H_0$. Using the latest supernova, BAO and CMB observations, we found a consistently low value of $q_0$ and strong inconsistency between angular-only BAO constraints and anisotropic BAO measurements, which are, or not, in agreement with CMB depending on the kind of analysis (see Table~$4$). We conclude that, in order to understand the reasons behind the $H_0$ crisis, a first step should be clarifying the tension between angular and perpendicular anisotropic BAO as this will help understanding if new physics is required at the pre-recombination epoch or/and during the dark energy era.