Extracting the three- and four-graviton vertices from binary pulsars and coalescing binaries

TL;DR

This paper explores how measurements from binary pulsars and coalescing binaries can test the three- and four-graviton vertices predicted by General Relativity, using a Feynman graph-based post-Newtonian approach.

Contribution

It introduces a Feynman graph formulation of the post-Newtonian expansion to connect gravitational vertices with observable tests of GR, providing bounds from pulsar timing and lunar laser ranging.

Findings

Binary pulsar timing constrains three-graviton vertex deviations at 0.1%.

Lunar laser ranging bounds the three-graviton vertex at 0.02%.

Coalescing binaries cannot effectively constrain vertex deviations due to parameter degeneracies.

Abstract

Using a formulation of the post-Newtonian expansion in terms of Feynman graphs, we discuss how various tests of General Relativity (GR) can be translated into measurement of the three- and four-graviton vertices. In problems involving only the conservative dynamics of a system, a deviation of the three-graviton vertex from the GR prediction is equivalent, to lowest order, to the introduction of the parameter beta_{PPN} in the parametrized post-Newtonian formalism, and its strongest bound comes from lunar laser ranging, which measures it at the 0.02% level. Deviation of the three-graviton vertex from the GR prediction, however, also affects the radiative sector of the theory. We show that the timing of the Hulse-Taylor binary pulsar provides a bound on the deviation of the three-graviton vertex from the GR prediction at the 0.1% level. For coalescing binaries at interferometers we find that, because of degeneracies with other parameters in the template such as mass and spin, the effects of modified three- and four-graviton vertices is just to induce an error in the determination of these parameters and, at least in the restricted PN approximation, it is not possible to use coalescing binaries for constraining deviations of the vertices from the GR prediction.