Solar System constraints on renormalization group extended general relativity: The PPN and Laplace-Runge-Lenz analyses with the external potential effect

• Published in: Physical review. D 2016-10, Vol.94 (8), Article 084036
• Main Authors: Rodrigues, Davi C., Mauro, Sebastião, de Almeida, Álefe O. F.
• Format: Article
• Language: English
• Subjects: Dark matter; Formalism; Galaxies; Parameters; Relativity; Solar system; Theory of relativity
• ISSN: 2470-0010; 2470-0029
• DOI: 10.1103/PhysRevD.94.084036

General relativity extensions based on renormalization group effects are motivated by a known physical principle and constitute a class of extended gravity theories that have some unexplored unique aspects. In this work we develop in detail the Newtonian and post-Newtonian limits of a realization called renormalization group extended general relativity (RGGR). Special attention is given to the external potential effect, which constitutes a type of screening mechanism typical of RGGR. In the Solar System, RGGR depends on a single dimensionless parameter ν¯⊙, and this parameter is such that for ν¯⊙=0 one fully recovers GR in the Solar System. Previously this parameter was constrained to be |ν¯⊙|≲10−21, without considering the external potential effect. Here we show that under a certain approximation RGGR can be cast in a form compatible with the parametrized post-Newtonian (PPN) formalism, and we use both the PPN formalism and the Laplace-Runge-Lenz technique to put new bounds on ν¯⊙, either considering or not the external potential effect. With the external potential effect the new bound reads |ν¯⊙|≲10−16. We discuss the possible consequences of this bound on the dark matter abundance in galaxies.