The structure of the renormalization group equations for the low-energy effective theory of gravity coupled to a scalar field is presented. An approximate solution to these equations with a finite number of independent renormalized parameters can be found when the mass scale characteristic of the fluctuations in the geometry is much smaller than the Planck mass. The cosmological constant problem is reformulated in this context and some conditions on the matter field content and interactions required in order to have a sufficiently small cosmological constant are identified. ͓S0556-2821͑96͒06320-5͔

The general structure of the renormalization group equations for the low energy effective field theory formulation of pure gravity is presented. The solution of these equations takes a particular simple form if the mass scale of the effective theory is much smaller than the Planck mass (a possibility compatible with the renormalization of the effective theory). A theory with just one free renormalized parameter is obtained when contributions suppressed by inverse powers of the Planck mass are neglected.

A general discussion of the renormalization of the quantum theory of a scalar field as an effective field theory is presented. The renormalization group equations in a mass-independent renormalization scheme allow us to identify the possibility to go beyond the renormalizable φ 4 theory without losing its predictive power. It is shown that there is a minimal extension with just one additional free parameter (the mass scale of the effective theory expansion) and some of its properties are discussed. PACS number(s): 11.10.Hi

We show that it is possible to find an extension of the matter content of the standard model with a unification of gauge and Yukawa couplings reproducing their known values. The perturbative renormalizability of the model with a single coupling and the requirement to accomodate the known properties of the standard model fix the masses and couplings of the additional particles. The implications on the parameters of the standard model are discussed.