Spinning quadrupoles in effective field theories of gravity

We study the effect of the two independent parity-even cubic interactions $I_1 = {R^{\alpha \beta}}_{\mu \nu} {R^{\mu \nu}}_{\rho \sigma} {R^{\rho \sigma}}_{\alpha \beta}$ and $G_3 = I_1 -2 {R^{\mu \nu \alpha}}_\beta {R^{\beta \gamma}}_{\nu \sigma} {R^\sigma}_{\mu \gamma \alpha}$ on the spectrum of gravitational waves emitted in the quasi-circular inspiral phase of the merger of two spinning objects. Focusing on the aligned spin configuration, we extract the corrections to Newton's potential at linear order in the perturbations, using the four-point amplitude of the massive spinning objects evaluated in the Post-Minkowskian expansion. We then derive the modifications to the quadrupole moments at leading order in the cubic perturbations, using a five-point amplitude with emission of a soft graviton. These modified moments, along with the corresponding potentials, are then employed to calculate the power emitted by gravitational waves during the inspiral phase. Using these results, we determine the changes to the waveforms, up to linear order in spin, in the Stationary Phase Approximation. Finally, we comment on the relation between cubic and tidal perturbations.