Quantum gravity and space-time foam

This thesis argues that Hawking's model on space-time foam predicts, after several modifications, a cosmological constant of the observed order. Inconsistencies of Hawking's model that were pointed out by Christensen and Duff are removed. A mechanism is given that can be used to remove the Ostrogradski instability of the effective matter action. The modified space-time foam model of Hawking describes a space-time filled with a gas of microscopic black- and wormholes. It is noted that particles which fly through such a space-time are governed by different equations of motion than in vacuum, since they scatter with the Hawking radiation of the microscopic black-holes and they are additionally under a collective influence of the gravitational field on long time scales. Under the assumption that Hawking radiation restores any information that was removed by the black-holes, one can derive the Schrodinger equation at low energies if one puts a classical particle into the space-time foam. The space-time foam model implies topology changes of the space-time during the expansion of the universe. It is argued that ordinary quantum field theory on Lorentzian space-times is incompatible with such changes since they give rise to singularities. It is proposed that if a stochastic model with non-differentiable paths underlies quantum mechanics at small scales (the usual path integral formulation is restricted to differentiable paths) then this could be used near the singularities during a topology change of the space-time.