  There is an approximately 9% discrepancy, corresponding to 2.4sigma, between
two independent constraints on the expansion rate of the universe: one
indirectly arising from the cosmic microwave background and baryon acoustic
oscillations, and one more directly obtained from local measurements of the
relation between redshifts and distances to sources. We argue that by taking
into account the local gravitational potential at the position of the observer
this tension - strengthened by the recent Planck results - is partially
relieved and the concordance of the standard model of cosmology increased. We
estimate that measurements of the local Hubble constant are subject to a cosmic
variance of about 2.4% (limiting the local sample to redshifts z>0.010) or 1.3%
(limiting it to z>0.023), a more significant correction than that taken into
account already. Nonetheless, we show that one would need a very rare
fluctuation to fully explain the offset in the Hubble rates. If this tension is
further strengthened, a cosmology beyond the standard model may prove
necessary.
