Measuring the sound horizon and absolute magnitude of SNIa by maximizing
  the consistency between low-redshift data sets
  The comoving sound horizon at the baryon drag epoch, $r_{d}$, encapsulates
very important physical information about the pre-recombination era and serves
as a cosmic standard ruler. On the other hand, the absolute magnitude of
supernovae of Type Ia (SNIa), $M$, is pivotal to infer the distances to these
standard candles. Having access to (at least) one of these two quantities is
crucial to measure the Hubble parameter $H_0$ from BAO/SNIa data. In this work
we present a new method to measure how long is the cosmic ruler and how bright
are the standard candles independently from the main drivers of the $H_0$
tension, namely by avoiding (i) the use of CMB data; (ii) the calibration of
SNIa in the first steps of the cosmic distance ladder; and (iii) the assumption
of any concrete cosmological model. We only assume that SNIa can be safely
employed as standard candles and $r_d$ as a standard ruler, together with the
validity of the Cosmological Principle and the metric description of gravity,
with photons propagating in null geodesics and the conservation of the photon
number. Our method is based on the minimization of a loss function that
represents the level of inconsistency between the low-redshift data sets
employed in this study, to wit: SNIa, BAO and cosmic chronometers. In our main
analysis we obtain: $r_d=(146.0^{+4.2}_{-5.1})$ Mpc,
$M=-19.362^{+0.078}_{-0.067}$. The former is fully compatible with Planck's
$\Lambda$CDM best-fit cosmology, but still leaves plenty of room for new
physics before the decoupling, whereas our constraint on $M$ lies closer to the
value preferred by the concordance model, although it is only $\sim 1.4\sigma$
below the SH0ES measurement.
