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 beβ . 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.

Causality Constraints on Gravitational Effective Field Theories

“…[7,14]. Different from the dim-8 ones, the dim-6 operators start contributing to the inspiral waveform at 5PN order [14]. Note that the PN order counting here, different from Ref.…”

“…The EFT corrections on the PN inspiral waveform have been studied in Refs. [7,14]. Different from the dim-8 ones, the dim-6 operators start contributing to the inspiral waveform at 5PN order [14].…”

“…For related works see Refs. [12][13][14][15]. While we may be on the edge of constraining gravitational EFTs using GW observations, theoretical considerations also have significant impact.…”

“…The dim-6 operators typically dominate over the dim-8 ones in the EFT expansion and could contribute to inspiral waveforms at lower post-Newtonian (PN) order. While dim-6 operators could start contributing to the inspiral waveform at 5PN order [14], 3 orders lower than the dim-8 operators (see App. F), we can still use the constraints obtained in Ref.…”

Exponentiation of the leading eikonal with spin

“…In addition to the description of point particles, tidal effects -both with and without spin -are also describable using a quantum-field-theoretic approach [29][30][31][32][33].…”