  DeWitt's suggestion that the wave function of the universe should vanish at
the classical big-bang singularity is here considered within the framework of
one-loop quantum cosmology. For pure gravity at one loop about a flat
four-dimensional background bounded by a 3-sphere, three choices of boundary
conditions are considered: vanishing of the linearized magnetic curvature when
only transverse-traceless gravitational modes are quantized; a one-parameter
family of mixed boundary conditions for gravitational and ghost modes;
diffeomorphism invariant boundary conditions for metric perturbations and ghost
modes. A positive zeta(0) value in these cases ensures that, when the 3-sphere
boundary approaches zero, the resulting one-loop wave function approaches zero.
This property may be interpreted by saying that, in the limit of small
three-geometry, the resulting one-loop wave function describes a
singularity-free universe. This property holds for one-loop functional
integrals, which are not necessarily equivalent to solutions of the quantum
constraint equations.
