Renormalization group improved gravitational actions: A Brans-Dicke approach

Abstract

A new framework for exploiting information about the renormalization group (RG) behavior of gravity in a dynamical context is discussed. The Einstein-Hilbert action is RG improved by replacing Newton's constant and the cosmological constant by scalar functions in the corresponding Lagrangian density. The position dependence of G and $\ensuremath{\Lambda}$ is governed by a RG equation together with an appropriate identification of RG scales with points in spacetime. The dynamics of the fields G and $\ensuremath{\Lambda}$ does not admit a Lagrangian description in general. Within the Lagrangian formalism for the gravitational field they have the status of externally prescribed ``background'' fields. The metric satisfies an effective Einstein equation similar to that of Brans-Dicke theory. Its consistency imposes severe constraints on allowed backgrounds. In the new RG framework, G and $\ensuremath{\Lambda}$ carry energy and momentum. It is tested in the setting of homogeneous-isotropic cosmology and is compared to alternative approaches where the fields G and $\ensuremath{\Lambda}$ do not carry gravitating 4-momentum. The fixed point regime of the underlying RG flow is studied in detail.