  Based on general relativity, it can be argued that deviations from a uniform
Hubble flow should be thought of as variations in the Universe's expansion
velocity field, rather than being thought of as peculiar velocities with
respect to a uniformly expanding space. The aim of this paper is to use the
observed motions of galaxies to map out variations in the Universe's expansion,
and more importantly, to investigate whether real variations in the Hubble
expansion are detectable given the observational uncertainties. All-sky maps of
the observed variation in the expansion are produced using measurements
obtained along specific lines-of-sight and smearing them across the sky using a
Gaussian profile. A map is produced for the final results of the HST
Extragalactic Distance Scale Key Project for the Hubble constant, a comparison
map is produced from a set of essentially independent data, and Monte Carlo
techniques are used to analyse the statistical significance of the variation in
the maps. A statistically significant difference in expansion rate of 9
km/s/Mpc is found to occur across the sky. Comparing maps of the sky at
different distances appears to indicate two distinct sets of extrema with even
stronger statistically significant variations. Within our supercluster,
variations tend to occur near the supergalactic plane, and beyond our
supercluster, variations tend to occur away from the supergalactic plane.
Comparison with bulk flow studies shows some concordance, yet also suggests the
bulk flow studies may suffer confusion, failing to discern the influence of
multiple perturbations.
