Disformally coupled scalar fields and inspiralling trajectories

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.

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

“…We focus here on the early portion of the binary's inspiral, which is amenable to analytic methods, and will use a generalisation of the "nonrelativistic general relativity" (NRGR) approach [183][184][185][186][187][188][189][190][191][192][193][194][195] to perform our calculations. When read alongside existing spin-independent results [181,182,[196][197][198][199][200][201][202][203][204], the spin-orbit results of this paper offer a more complete picture of how these systems behave in scalar-tensor gravity.…”

“…where ˆ is the unit vector in the direction of L. Notice that there are no disformal spinindependent terms in the above result, as these vanish for circular orbits [181,182]. A more useful result to have is the inverse of this relation, which reads…”

“…Now is a good time to mention that the two powers of the orbital eccentricity e, which appear in the third row of table 1, do not arise automatically from the power-counting rules, but have been included by hand to reflect the results of more detailed calculations, which show that disformal spin-independent effects actually vanish in the limit of a circular orbit [181,182]. With this factor included, we see that L is always accompanied by either e 2 or S when it appears in a Feynman diagram; hence, the necessary and sufficient conditions that justify truncating some quantity to linear order in L are L e 2 1 and L S 1.…”

“…The leading contribution to the disformal spin-independent sector was recently calculated in ref. [182], albeit only for the special case in which α 1 = α 2 and β 1 = β 2 . It is nevertheless straightforward to repeat the calculation with arbitrary coefficients, in which case one finds…”

Disformal couplings in a $Λ$CDM background cosmology

“…The occurence of the disformal relation happens in many theories such as Horndeski-type scalar tensor theory [20], non-linear massive gravity theory [21,22], brane cosmology with higher dimensions [23]. The disformal framework has attracted considerable attention lately [19,[24][25][26].…”