  The influence of a spherical boundary on the vacuum fluctuations of a massive
scalar field is investigated in background of $(D+1)$-dimensional Milne
universe, assuming that the field obeys Robin boundary condition on the sphere.
The normalized mode functions are derived for the regions inside and outside
the sphere and different vacuum states are discussed. For the conformal vacuum,
the Hadamard function is decomposed into boundary-free and sphere-induced
contributions and an integral representation is obtained for the latter in both
the interior and exterior regions. As important local characteristics of the
vacuum state the vacuum expectation values (VEVs) of the field squared and of
the energy-momentum tensor are investigated. It is shown that the vacuum
energy-momentum tensor has an off-diagonal component that corresponds to the
energy flux along the radial direction. Depending on the coefficient in Robin
boundary condition the sphere-induced contribution to the vacuum energy and the
energy flux can be either positive or negative. At late stages of the expansion
and for a massive field the decay of the sphere-induced VEVs, as functions of
time, is damping oscillatory. The geometry under consideration is conformally
related to that for a static spacetime with negative constant curvature space
and the sphere-induced contributions in the corresponding VEVs are compared.
