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 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 , and this parameter is such that for one fully recovers GR in the Solar System. Previously this parameter was constrained to be , 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 , either considering or not the external potential effect. With the external potential effect the new bound reads . We discuss the possible consequences of this bound on the dark matter abundance in galaxies.
- Received 18 September 2016
DOI:https://doi.org/10.1103/PhysRevD.94.084036
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