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

TL;DR

This paper investigates how a modified gravity theory based on Renormalization Group effects behaves in the Solar System, deriving new constraints on its parameters using PPN and orbital analyses, with implications for dark matter.

Contribution

It develops the Newtonian and post-Newtonian limits of RG extended General Relativity and derives new bounds on its key parameter considering the external potential effect.

Findings

The external potential effect weakens the constraints on the RGGR parameter.

RGGR can be compatible with PPN formalism under certain approximations.

New bounds on the RGGR parameter are established, $|ar u_ on| \,\lesssim\, 10^{-16}$.

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.