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An explicit expression is derived for the quantum gravitational vacuum state by use of the saddle-point approximation and a conformally invariant action. It consists of a superposition of zero-energy classical vacua that differ in the topology both of the local Lorentz frames (leading to CP nonconservation) and of space itself. Space is found to have Planck-size wormholes and spinorial knots, and is surrounded by a vapor of disconnected submanifolds. The scattering matrix constructed on this vacuum is not unitary but the superscattering matrix conserves probability.
Andrew Strominger (Mon,) studied this question.