Without strong a priori constraints on the density structure of the Universe we cannot exclude the possibility that the local value of the expansion rate is different from the global rate. Constraints exist from the velocity field and from the isotropy of the microwave background radiation, however. For the sake of definiteness we can hypothesize a bubble model in which the expansion rate is 75 km/sec/Mpc locally but 50 km/sec/Mpc outside the radius of Coma.
Figure 5 shows two of the largest scale velocity field constraints on this
model. The data offer no support for 
= 0.5 at or around the
velocity of Coma.
Figure 5:
Deviations from a uniform Hubble flow. Solid circles: clusters
of galaxies with Tully-Fisher distances. Solid triangles: EPM data of
Schmidt et al. (1994). Open symbols: brightest cluster
members from Lauer & Postman (1994). There is no evidence that a different
value of the Hubble Constant pertains inside and outside the distance of
the Coma cluster at v
= 7200 km/sec.
We might also expect perturbations of this size to make a strong imprint on
the microwave background radiation, as Silk has pointed out at this
meeting. A velocity perturbation of 
0.5 is three times
the velocity perturbation seen in the vicinity of the Great Attractor. It
follows that in such a bubble
But this value of 
implies
according to Bertschinger, Gorski & Dekel (1990), if 
= 1. Under that
condition the anisotropy would be detected on 1
scales. For
= 0.1 the anisotropy would appear on 12
scales. Currently
detection has been achieved at this level and on these scales in both the
Python and OVRO experiments (Dragovan 1995, Myers 1995). But anisotropies
as large as the bubble model imply 3
abnormalities. The bubble we
are hypothesizing would therefore be an extremely rare place for us to find
ourselves in, unless the Universe is open (Fullana et al. 1994).
Acknowledgements
I would like to thank Brian Schmidt for providing Figure 4.