Local determination of the Hubble constant and the deceleration
  parameter
  The determination of the Hubble constant $H_0$ from the Cosmic Microwave
Background by the Planck Collaboration [Aghanim et al. 2018] is in tension at
$4.2\sigma$ with respect to the local determination of $H_0$ by the SH0ES
collaboration [Reid et al. 2019]. Here, we improve upon the local
determination, which fixes the deceleration parameter to the standard
$\Lambda$CDM model value of $q_0=-0.55$, that is, uses information from
observations beyond the local universe. First, we derive the effective
calibration prior on the absolute magnitude $M_B$ of Supernovae Ia, which can
be used in cosmological analyses in order to avoid the double counting of
low-redshift supernovae. We find $M_B = -19.2334 \pm 0.0404$ mag. Then, we use
the above $M_B$ prior in order to obtain a determination of the local $H_0$
which only uses local observations and only assumes the cosmological principle,
that is, large-scale homogeneity and isotropy. This is achieved by adopting an
uninformative flat prior for $q_0$ in the cosmographic expansion of the
luminosity distance. We use the latest Pantheon sample and find $H_0= 75.35 \pm
1.68 \text{ km s}^{-1} {\rm Mpc}^{-1}$, which features a 2.2% uncertainty,
close to the 1.9% error obtained by the SH0ES Collaboration. Our determination
is at the higher tension of $4.5\sigma$ with the latest results from the Planck
Collaboration that assume the $\Lambda$CDM model. Furthermore, we also
constrain the deceleration parameter to $q_0= -1.08 \pm 0.29$, which disagrees
with Planck at the $1.9\sigma$ level. These estimations only use supernovae in
the redshift range $0.023\le z\le 0.15$.
