# Disformally Coupled Scalar Fields and Inspiralling Trajectories

## TL;DR

This paper investigates how nearly massless scalar fields with conformal and disformal couplings influence the dynamics of inspiralling binary systems, providing new corrections to the energy and emission formulas relevant for gravitational wave observations.

## Contribution

It derives the first disformal correction to the Einstein-Infeld-Hoffmann Lagrangian using both the Fokker method and Effective Field Theory, and explores observational bounds from binary pulsar data.

## Key findings

- Disformal corrections appear at 2PN order for eccentric orbits.
- Corrections vanish for circular orbits up to 7PN order.
- Eccentric orbit monitoring can constrain disformal couplings.

## Abstract

We show how a nearly massless scalar field conformally and disformally coupled to matter can affect the dynamics of two bodies in their inspiralling phase before merging. We discuss both the conservative dynamics, e.g. how the energy of the bound system is corrected by the conformal and disformal interactions, and the dissipative part where scalars and gravitons are emitted. The first disformal correction to the Einstein-Infeld-Hoffmann Lagrangian is obtained using both the Fokker method relying on the equations of motion and an Effective Field Theory approach using Feynman diagrams. This leads to a correction to the energy functional at the 2PN level for eccentric orbits, which vanishes for circular orbits up to the 7PN order. The dissipative power from the disformal interaction gives a correction to the monopole and quadrupole terms in the presence of a conformal coupling. Although this correction vanishes for circular orbits at leading order, this is not the case for elliptical orbits allowing us to derive a bound on the disformal coupling from the time drift of the period for the Hulse-Taylor binary pulsar, which is slightly stronger than the one from fifth force tests. We conclude that the prospect of observing disformal effects for inspiralling systems lies in the accurate monitoring of eccentric trajectories as expected for the LISA experiment.