Renormalization group flow in scalar-tensor theories: I

We study the renormalization group flow in a class of scalar-tensor theories involving at most two derivatives of the fields. We show in general that minimal coupling is self-consistent, in the sense that when the scalar self-couplings are switched off, their beta functions also vanish. Complete, explicit beta functions that could be applied to a variety of cosmological models are given in a five-parameter truncation of the theory in d = 4. In any dimension d > 2 we find that the flow has only a 'Gaussian Matter' fixed point, where all scalar self-interactions vanish but Newton's constant and the cosmological constant are nontrivial. The properties of these fixed points can be studied algebraically to some extent. In d = 3 we also find a gravitationally dressed version of the Wilson-Fisher fixed point, but it seems to have unphysical properties. These findings are in accordance with the hypothesis that these theories are asymptotically safe.