  We analyse the impact of various boundary conditions on the (minisuperspace)
Lorentzian gravitational path integral. In particular we assess the
implications for the Hartle-Hawking no-boundary wavefunction. It was shown
recently that when this proposal is defined as a sum over compact metrics,
problems arise with the stability of fluctuations. These difficulties can be
overcome by an especially simple implementation of the no-boundary idea: namely
to take the Einstein-Hilbert action at face value while adding no boundary
term. This prescription simultaneously imposes an initial Neumann boundary
condition for the scale factor of the universe and, for a Bianchi IX spacetime,
Dirichlet conditions for the anisotropies. Another way to implement the
no-boundary wavefunction is to use Robin boundary conditions. A sub-class of
Robin conditions allows one to specify the Hubble rate on the boundary
hypersurface, and we highlight the surprising aspect that specifying the final
Hubble rate (rather than the final size of the universe) significantly alters
the off-shell structure of the path integral. The conclusion of our
investigations is that all current working examples of the no-boundary
wavefunction force one to abandon the notion of a sum over compact and regular
geometries, and point to the importance of an initial Euclidean momentum.
