Model independent $H(z)$ reconstruction using the cosmic inverse
  distance ladder
  Recent distance ladder determinations of the Hubble constant $H_0$ disagree
at about the $3.5\sigma$ level with the value determined from Planck
measurements of the cosmic microwave background (CMB) assuming a $\Lambda$CDM
cosmology. This discrepancy has prompted speculation that new physics might be
required beyond that assumed in the $\Lambda$CDM model. In this paper, we apply
the inverse distance ladder to fit a parametric form of $H(z)$ to baryon
acoustic oscillation (BAO) and Type Ia supernova data together with priors on
the sound horizon at the end of the radiation drag epoch, $r_d$. We apply
priors on $r_d$, based on inferences from either Planck or the Wilkinson
Microwave Anistropy Probe (WMAP), and demonstrate that these values are
consistent with CMB-independent determinations of $r_d$ derived from
measurements of the primordial deuterium abundance, BAO and supernova data
assuming the $\Lambda$CDM cosmology. The $H(z)$ constraints that we derive are
independent of detailed physics within the dark sector at low redshifts,
relying only on the validity of the Friedmann-Robertson-Walker (FRW) metric of
General Relativity. For each assumed prior on $r_d$, we find consistency with
the inferred value of $H_0$ and the Planck $\Lambda$CDM value and corresponding
tension with the distance ladder estimate.
