Recent observations of high-redshift supernovae seem to suggest that the
global geometry of the Universe may be affected by a `cosmological constant',
which acts to accelerate the expansion rate with time. But these data by
themselves still permit an open universe of low mass density and no
cosmological constant. Here we derive an independent constraint on the lower
bound to the mass density, based on deviations of galaxy velocities from a
smooth universal expansion. This constraint rules out a low-density open
universe with a vanishing cosmological constant, and together the two favour a
nearly flat universe in which the contributions from mass density and the
cosmological constant are comparable. This type of universe, however, seems to
require a degree of fine tuning of the initial conditions that is in apparent
conflict with `common wisdom'.Comment: 8 pages, 1 figure. Slightly revised version. Letter to Natur