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arXiv · hep-th/0311196

Renormalization group improved gravitational actions: a Brans-Dicke approach

M. Reuter·H. Weyer
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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 $Λ$ 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 $Λ$ 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 $Λ$ 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 $Λ$ do not carry gravitating 4-momentum. The fixed point regime of the underlying RG flow is studied in detail.

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M. Reuter, H. Weyer. 2004-03-23. Renormalization group improved gravitational actions: a Brans-Dicke approach. https://doi.org/10.1103/physrevd.69.104022

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