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Recent distance ladder determinations of the Hubble constant $H_0$ disagreeat about the $3.5\sigma$ level with the value determined from Planckmeasurements of the cosmic microwave background (CMB) assuming a $\Lambda$CDMcosmology. This discrepancy has prompted speculation that new physics might berequired beyond that assumed in the $\Lambda$CDM model. In this paper, we applythe inverse distance ladder to fit a parametric form of $H(z)$ to baryonacoustic oscillation (BAO) and Type Ia supernova data together with priors onthe sound horizon at the end of the radiation drag epoch, $r_d$. We applypriors on $r_d$, based on inferences from either Planck or the WilkinsonMicrowave Anistropy Probe (WMAP), and demonstrate that these values areconsistent with CMB-independent determinations of $r_d$ derived frommeasurements of the primordial deuterium abundance, BAO and supernova dataassuming the $\Lambda$CDM cosmology. The $H(z)$ constraints that we derive areindependent of detailed physics within the dark sector at low redshifts,relying only on the validity of the Friedmann-Robertson-Walker (FRW) metric ofGeneral Relativity. For each assumed prior on $r_d$, we find consistency withthe inferred value of $H_0$ and the Planck $\Lambda$CDM value and correspondingtension with the distance ladder estimate.

Model independent $H(z)$ reconstruction using the cosmic inverse distance ladder