From amplitudes to gravitational radiation with cubic interactions and tidal effects

Abstract: We study the effect of cubic and tidal interactions on the spectrum of gravitational waves emitted in the inspiral phase of the merger of two non-spinning objects. There are two independent parity-even cubic interaction terms, which we take to be $I_1 = {R^{\alpha \beta}}{\mu \nu} {R^{\mu \nu}}{\rho \sigma} {R^{\rho \sigma}}{\alpha \beta}$ and $G_3 = I_1-2 R^{\alpha}\,{\mu}\,^{\beta}\,_{\nu} R^{\mu}\,{\rho}\,^{\nu}\,{\sigma} R^{\rho}\,{\alpha}\,^{\sigma}\,{\beta}$. The latter has vanishing pure graviton amplitudes but modifies mixed scalar/graviton amplitudes which are crucial for our study. Working in an effective field theory set-up, we compute the modifications to the quadrupole moment due to $I_1$, $G_3$ and tidal interactions, from which we obtain the power of gravitational waves radiated in the process to first order in the perturbations and leading order in the post-Minkowskian expansion. The $I_1$ predictions are novel, and we find that our results for $G_3$ are related to the known quadrupole corrections arising from tidal perturbations, although the physical origin of the $G_3$ coupling is unrelated to the finite-size effects underlying tidal interactions. We show this by recomputing such tidal corrections and by presenting an explicit field redefinition. In the post-Newtonian expansion our results are complete at leading order, which for the gravitational-wave flux is 5PN for $G_3$ and tidal interactions, and 6PN for $I_1$. Finally, we compute the corresponding modifications to the waveforms.