Solar System constraints on Renormalization Group extended General Relativity: The PPN and Laplace-Runge-Lenz analyses with the external potential effect

Abstract

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 realisation called Renormalization Group extended General Relativity (RGGR). Special attention is taken 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 ${\bar{\nu }}_{\odot }$, and this parameter is such that for ${\bar{\nu }}_{\odot }=0$ one fully recovers GR in the Solar System. Previously this parameter was constrained to be $|{\bar{\nu }}_{\odot }|\lesssim 10^{-21}$, without considering the external potential effect. Here we show that under a certain approximation RGGR can be cast in a form compatible with the Parametrised Post-Newtonian (PPN) formalism, and we use both the PPN formalism and the Laplace-Runge-Lenz technique to put new bounds on ${\bar{\nu }}_{\odot }$, either considering or not the external potential effect. With the external potential effect the new bound reads $|{\bar{\nu }}_{\odot }|\lesssim 10^{-16}$. We discuss the possible consequences of this bound to the dark matter abundance in galaxies.

13 pages, 4 figures. Added references and minor corrections in text. Version to appear in PRD

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