Post-Einsteinian tests of linearized gravitation

TL;DR

This paper proposes an extension to general relativity by introducing scale-dependent coupling constants, leading to testable deviations in solar system phenomena such as light deflection and spacecraft trajectories.

Contribution

It introduces a modified linearized gravitational framework with two running coupling constants, extending the PPN formalism while remaining compatible with existing solar system tests.

Findings

Predicts a Pioneer-like anomaly for eccentric probes.

Suggests a range dependence of Eddington parameter gamma.

Extends PPN framework with scale-dependent couplings.

Abstract

The general relativistic treatment of gravitation can be extended by preserving the geometrical nature of the theory but modifying the form of the coupling between curvature and stress tensors. The gravitation constant is thus replaced by two running coupling constants which depend on scale and differ in the sectors of traceless and traced tensors. When calculated in the solar system in a linearized approximation, the metric is described by two gravitation potentials. This extends the parametrized post-Newtonian (PPN) phenomenological framework while allowing one to preserve compatibility with gravity tests performed in the solar system. Consequences of this extension are drawn here for phenomena correctly treated in the linear approximation. We obtain a Pioneer-like anomaly for probes with an eccentric motion as well as a range dependence of Eddington parameter $\gamma$ to be seen in light deflection experiments.