  We construct exact nonstatic nonhomogeneous spherically symmetric solutions
in the theory of gravity with a scalar field possessing the exponential
potential. The solution of particular interest corresponds to the scalar field
with negative kinetic energy, i.e. a ghost, and represents two asymptotically
homogeneous spatially flat universes connected by a throat. We interpret this
solution as a wormhole in cosmological setting. Both the universes and the
wormhole throat are simultaneously expanding with acceleration. The character
of expansion qualitatively depends on the wormhole's mass $m$. For $m=0$ the
expansion goes exponentially, so that the corresponding spacetime configuration
represents two de Sitter universes joining by the throat. For $m>0$ the
expansion has the power character, so that one has the inflating wormhole
connecting two homogeneous spatially flat universes expanding according to the
power law into the final singularity. The stability analysis of the non-static
wormholes reveals their instability against linear spherically symmetric
perturbations.
