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 $\Lambda$ 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 $\Lambda$ 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 $\Lambda$ 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 $\Lambda$ do not carry gravitating 4-momentum. The fixed point regime of the underlying RG flow is studied in detail.

• Received 21 November 2003

DOI:https://doi.org/10.1103/PhysRevD.69.104022