Gravity tests and the Pioneer anomaly

TL;DR

This paper proposes a metric extension of general relativity with scale-dependent coupling constants to explain the Pioneer anomaly while remaining consistent with existing solar system gravity tests.

Contribution

It introduces a post-Einsteinian extension of gravity that modifies the coupling between curvature and stress tensors, potentially explaining the Pioneer anomaly.

Findings

The extended theory can account for the Pioneer anomaly.

It remains compatible with existing gravity tests.

The theory suggests new experimental tests or reanalysis of existing data.

Abstract

Experimental tests of gravity performed in the solar system show a good agreement with general relativity. The latter is however challenged by the Pioneer anomaly which might be pointing at some modification of gravity law at ranges of the order of the size of the solar system. We introduce a metric extension of general relativity which, while preserving the equivalence principle, modifies the coupling between curvature and stress tensors and, therefore, the metric solution in the solar system. The ``post-Einsteinian extension'' replaces Newton gravitation constant by two running coupling constants, which depend on the scale and differ in the sectors of traceless and traced tensors, so that the metric solution is characterized by two gravitation potentials. The extended theory has the capability to preserve compatibility with gravity tests while accounting for the Pioneer anomaly. It can also be tested by new experiments or, maybe, by having a new look at data of already performed experiments.