  The transition from the quantum to the classical regime of the nucleation of
the closed Robertson-Walker Universe with spacially homogeneous matter fields
is investigated with a perturbation expansion around the sphaleron
configuration. A criterion is derived for the occurrence of a first-order type
transition, and the related phase diagram for scalar and vector fields is
obtained. For scalar fields both the first and second order transitions can
occur depending on the shape of the potential barrier. For a vector field, here
that of an O(3) nonlinear $\sigma$-model, the transition is seen to be only of
the first order.
