Integration contours for the no-boundary wave function of the universe

In the no-boundary proposal for the initial conditions of a closed cosmology, the wave function of the universe is the integral of exp(-action) over a contour of four-geometries and matter-field configurations on compact manifolds having only that boundary necessary to specify the arguments of the wave function. There is no satisfactory covariant Hamiltonian quantum mechanics of closed cosmologies from which the contour may be derived, as there would be for defining the ground states of asymptotically flat spacetimes. No compelling prescription, such as the conformal rotation for asymptotically flat spacetimes, has been advanced. In this paper it is argued that the contour of integration can be constrained by simple physical considerations: (1) the integral defining the wave function should converge; (2) the wave function should satisfy the constraints implementing diffeomorphism invariance; (3) classical spacetime when the universe is large should be a prediction; (4) the correct field theory in curved spacetime should be reproduced in this spacetime; (5) to the extent that wormholes make the cosmological constant dependent on initial conditions the wave function should predict its vanishing