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Time-dependent wormhole solutions are found which evolve in a
cosmological background. Solutions are presented both for GR and
Brans-Dicke field equations. Conditions are derived for the
supporting matter to be non-exotic. The traceless energy-momentum
tensor needed to support the geometry is in the form of an
anisotropic fluid. Far from the wormhole, the equation of state
rapidly approaches that of an isotropic perfect fluid with
$\emph{p}=\frac{1}{3}\rho$. For the BD wormholes we obtain
$\rho=0$ everywhere, except for the $n= const.limit$, in which
case the GR results are reproduced.
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