  The universe is viewed as a dust gas filling a sphere and floating in
infinite empty space. Einstein's gravitational equations are applied to this
case together with appropriate boundary values. The equations are solved for
initial conditions chosen so as to describe the observed Hubble diagram. We
find that the solution is not unique so that more astronomical observations are
needed. However, those solutions which were found do not exhibit an accelerated
expansion of the universe, nor -- obviously then -- do they need the notion of
a dark energy driving such an expansion.
  We present this study as an alternative to the prevailing Robertson-Walker
cosmology.
