Spin-orbit effects for compact binaries in scalar-tensor gravity

TL;DR

This paper develops an effective field theory framework to analyze spin-orbit effects in scalar-tensor gravity for binary systems, revealing that disformal couplings can significantly influence gravitational wave signals.

Contribution

It introduces a comprehensive model for spinning bodies coupled to scalar fields, showing how scalar coupling affects spin-orbit interactions and gravitational wave phase evolution.

Findings

Disformal spin-orbit effects can dominate over conformal effects due to large prefactors.

Spin-orbit effects enter gravitational wave phase at 0.5PN or 1.5PN order for conformal coupling.

Disformal effects start at 3.5PN or 4.5PN order but can be more significant in certain regimes.

Abstract

Gravitational waves provide us with a new window into our Universe, and have already been used to place strong constrains on the existence of light scalar fields, which are a common feature in many alternative theories of gravity. However, spin effects are still relatively unexplored in this context. In this work, we construct an effective point-particle action for a generic spinning body that can couple both conformally and disformally to a real scalar field, and we show that requiring the existence of a self-consistent solution automatically implies that if a scalar couples to the mass of a body, then it must also couple to its spin. We then use well-established effective field theory techniques to conduct a comprehensive study of spin-orbit effects in binary systems to leading order in the post-Newtonian (PN) expansion. Focusing on quasicircular nonprecessing binaries for simplicity, we systematically compute all key quantities, including the conservative potential, the orbital binding energy, the radiated power, and the gravitational-wave phase. We show that depending on how strongly each member of the binary couples to the scalar, the spin-orbit effects that are due to a conformal coupling first enter into the phase at either 0.5PN or 1.5PN order, while those that arise from a disformal coupling start at either 3.5PN or 4.5PN order. This suppression by additional PN orders notwithstanding, we find that the disformal spin-orbit terms can actually dominate over their conformal counterparts due to an enhancement by a large prefactor. Accordingly, our results suggest that upcoming gravitational-wave detectors could be sensitive to disformal spin-orbit effects in double neutron star binaries if at least one of the two bodies is sufficiently scalarised.