RENORMALIZATION-GROUP FOR NONRENORMALIZABLE THEORIES - EINSTEIN GRAVITY WITH A SCALAR FIELD

We develop a renormalization-group formalism for nonrenormalizable the ories and apply it to Einstein gravity theory coupled to a scalar fiel d with the Lagrangian L = square-root g[RU(phi) -1/2 G(phi)g(munu) par tial derivative(mu)phi partial derivative(nu)phi - V(phi)] where U(phi ), G(phi), and V(phi) are arbitrary functions of the scalar field. We calculate the one-loop counterterms of this theory and obtain a system of renormalization-group equations in partial derivatives for the fun ctions U, G, and V playing the role of generalized charges which subst itute for the usual charges in multicharge theories. In the limit of a large but slowly varying scalar field and small spacetime curvature t his system gives the asymptotic behavior of the generalized charges co mpatible with the conventional choice of these functions in quantum co smological applications. It also demonstrates in the over-Planckian do main the existence of the Weyl-invariant phase of gravity theory asymp totically free in gravitational and cosmological constants.