Radiation reaction force for scalar-tensor theories in effective-one-body formalism

TL;DR

The paper addresses how to extend the EOB framework to nonspinning binaries in massless scalar-tensor theories on eccentric orbits, deriving the radiation-reaction force up to $1.5\mathrm{PN}$ by combining energy-momentum balance with Schott terms. It provides a detailed map of fluxes and dynamical quantities across harmonic, ADM, and EOB coordinates up to $2\mathrm{PN}$, and constructs a Schott-term Ansatz that accounts for dipolar radiation, fixing all unknown coefficients by circular-orbit limits. The main results include explicit expressions for the RR force at $-1\mathrm{PN}$, Newtonian, and $0.5\mathrm{PN}$ orders, and a demonstration that, unlike GR, ST theories have no residual gauge freedom at $1.5\mathrm{PN}$, leading to a unique RR description in the EOB framework. These developments enable ST-corrected, eccentric GW templates suitable for tests of gravity with upcoming detectors. The work thus advances waveform modeling in alternative theories and supports robust, bias-resistant GW tests of GR in the strong-field, high-curvature regime.

Abstract

Whilst most of the binary configurations in modified theories of gravity are studied under quasi-circular orbit limit, eccentricity effects could play a significant role in future gravitational wave detections. We derive the gravitational radiation-reaction force for nonspinning eccentric orbits within the effective-one-body (EOB) description for the massless scalar-tensor theories up to 1.5 post-Newtonian (PN) order. The effects in such theories start at $1/c^3$ and interestingly, the 1.5PN order effect is due to the radiation reaction square effects which is a conservative effect. The results derived here can be implemented in the quasi-circular EOB-based waveform models to construct waveform templates for generic orbit binaries within massless scalar-tensor theories of gravity.