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.
