Renormalization group improved gravitational actions: A Brans-Dicke approach

By Martin Reuter, H. Weyer. 2003

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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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/0880cca12829f26306b1d4866b151e57cafef6a3

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Citations in the corpus

Categorizing Different Approaches to the Cosmological Constant Problem (2004, methodology): “measured as a quintessence of phantom dark energy and be consistent with all data, as long as 0 ≤ |ν| ≪ 1 [151]. As a solution to the cosmological constant problem, it obviously cannot help. In refs. [152, 149], it is argued that there may be a UV ﬁxed point at which gravity becomes asymptotically f”
Galaxy Rotation Curves without Nonbaryonic Dark Matter (2005, methodology): “A renormalization group (RG) framework (Reuter & Weyer 2004a, 2004b) for MSTGwas developed to describe the running of the effective gravitational coupling constant G and the effective coupling constant c, which measures the strength of the coupling of theF k field tomatter.”
The Asymptotic Safety Scenario in Quantum Gravity (2006, methodology): “For an illustration [189, 191, 190] consider a truncated solution of the FRGE (C.”
Galaxy cluster masses without non-baryonic dark matter (2005, methodology): “A renormalization group (RG) framework (Reuter & Weyer 2004a,b) for MSTG was developed to describe the running of the effective gravitational coupling constant G, and the effective coupling constant γ c that measures the strength of the coupling of the Fμνλ field to matter.”