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

TL;DR

The paper develops a gauge-invariant, EFT-based framework to quantify deviations from General Relativity in the non-linear graviton sector by introducing parameters $\beta_3$ and $\beta_4$ for the three- and four-graviton vertices. It shows that, in the conservative 1PN regime, $\beta_3$ maps to $\beta_{\rm PPN}=1+\beta_3$, while radiative-sector effects enable direct bounds from binary pulsars; however, coalescing binaries observed by GW interferometers suffer degeneracies with masses and spins that preclude constraining the vertices in the restricted PN approach. Solar-system tests (notably lunar laser ranging) bound $|\beta_3|$ at the $2\times10^{-4}$ level, and the Hulse-Taylor pulsar bound lies near $0.1\%$, e.g. $\beta_3=(4.0\pm6.4)\times10^{-4}$, reflecting sensitivity to the radiative sector. The study concludes that interferometers cannot currently measure the three- and four-graviton vertices within this framework, though including higher PN harmonics might help break degeneracies; the work provides a clear, phenomenological method for testing GR's non-linear structure analogous to particle-physics vertex tests.

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.

Figures (5)

• Figure 1: The diagrams that give the terms proportional to $G_N^2$ in the 1PN Lagrangian. Dashed lines denote potential gravitons, solid lines the point-like sources.
• Figure 2: The diagrams that contribute to the matter-radiation Lagrangian. Dashed lines denote potential gravitons, wiggly lines radiation gravitons, and solid lines the point-like sources.
• Figure 3: The self-energy diagrams whose imaginary part gives the radiated power. The wiggly line can refer either to $h_{ij}$ or to $h_{00}$, and the vertices to any of the four $I^a_{ij}S^a_{ij}$ with $a=1,\ldots,4$, see the text.
• Figure 4: The diagrams that contribute to the conservative dynamics, which are affected by a modification of the four-graviton vertex.
• Figure 5: The diagram that contributes to the radiative dynamics, which is affected by a modification of the four-graviton vertex.