On A Possible Ground State for Quantum Gravity

Abstract

A variational calculation is presented of the ADM-energy of the quantized gravitational field around a wormhole solution of the classical Einstein's equations. One finds the energy of such state to be in general lower than the perturbative ground state, in which the quantized gravity field fluctuates around flat (Euclidean) space-time. As a result the strong indication emerges that a gas (or a lattice) of wormholes of Planck mass and average distance $l_p$, the Planck length, may be a good approximation of the Ground State of Quantum Gravity, some implications of which are reviewed.