Mean-field quantum gravity

We describe a new approach to quantum gravity, based on a kind of mean-field approximation. The action, which we choose to be quadratic in curvature and torsion, is made polynomial by replacing the inverse vierbein by its mean value. This action is used to compute the effective action for the vierbein and hence its vacuum expectation value. Self-consistency is then enforced by requiring that this vacuum expectation value be proportional to the mean field. We have explicitly carried out this self-consistent procedure at one loop in the case of a mean field corresponding to Minkowski space, de Sitter space, and in the long-wavelength limit for a generic space. General relativity is recovered as a low-energy approximation.