Post-Einsteinian tests of gravitation

TL;DR

This paper explores extended theories of gravity beyond Einstein's general relativity, introducing scale-dependent couplings, analyzing their effects on solar system phenomena, and assessing their ability to explain anomalies like the Pioneer anomaly while remaining consistent with planetary tests.

Contribution

It develops a framework for post-Einsteinian gravity theories with scale-dependent couplings and evaluates their phenomenological implications, including compatibility with solar system tests and anomalies.

Findings

Some extended theories can explain the Pioneer anomaly.

Certain modifications remain compatible with planetary motion tests.

PPN extensions do not meet the compatibility criteria.

Abstract

Einstein gravitation theory can be extended by preserving its geometrical nature but changing the relation between curvature and energy-momentum tensors. This change accounts for radiative corrections, replacing the Newton gravitation constant by two running couplings which depend on scale and differ in the two sectors of traceless and traced tensors. The metric and curvature tensors in the field of the Sun, which were obtained in previous papers within a linearized approximation, are then calculated without this restriction. Modifications of gravitational effects on geodesics are then studied, allowing one to explore phenomenological consequences of extensions lying in the vicinity of general relativity. Some of these extended theories are able to account for the Pioneer anomaly while remaining compatible with tests involving the motion of planets. The PPN Ansatz corresponds to peculiar extensions of general relativity which do not have the ability to meet this compatibility challenge.