Post-Newtonian, quasicircular binary inspirals in quadratic modified gravity

Abstract

In this erratum, we point out that the correction to the gravitational energy flux from compact binary inspirals in dynamical Chern-Simons gravity enters at third post-Newtonian order instead of second post-Newtonian order. We also correct the scalar energy flux at second post-Newtonian order by considering terms that we missed in the original paper. I. GRAVITATIONAL RADIATIONIn [1], we claimed that the correction to the gravitational energy flux, i.e. the energy flux from binary inspirals induced by the metric perturbation in dynamical Chern-Simons (dCS) gravity, enters at second post-Newtonian (2PN) order. Here, we point out that there are terms that we overlooked, and if we take these terms into account properly, the 2PN terms cancel and the correction enters at 3PN order. where h μν and h μν are the general relativity (GR) and dCS metric perturbations, respectively. We worked in harmonic gauge, h μν ;ν ¼ 0 ¼h μν ;ν , where we defined the metric perturbations viāWe then expanded the modified Einstein equations, focusing on the dCS correction and keeping terms up to linear order in h μν andh μν ,where □ η is the d'Alembertian operator of flat spacetime and 1 Recall that a term in an expression is said to be of Nth PN order if it is proportional to v 2N relative to the leading-order term in that same expression.

Further Investigations

“…To show that we can nevertheless be sensitive to anomalies at higher PN order, we now consider signals with a constant shift at 2PN. We note in passing that theories with quadratic curvature terms in the action tend to introduce extra contributions at 2PN [66,67,68].…”

“…Setting δχ 4 = 0.2, the induced change in phase at f = 150 Hz is comparable to a constant shift δχ 3 = −0.035 at 1.5PN, namely 4.5 radians. The choice of a modification at 2PN was inspired by corrections to the phase if one considers a modified Einstein-Hilbert action containing terms that are quadratic in the Riemann tensor, as calculated in [66,67,68]. As can be seen from Fig.…”

Scientific Potential of Decigo Pathfinder and Testing Gr With Space-Borne Gravitational Wave Interferometers

“…The gravitational and scalar radiation energy flux in quadratic gravity are calculated in Ref. 300 within the post-Newtonian approach. In the even parity sector, the scalar dipole radiation exists, just like in BD theory, and this gives -1PN dissipative correction to the gravitational waveform phase relative to GR.…”

“…As for the odd parity sector of quadratic gravity (dynamical CS gravity), both scalar radiation and corrections to the gravitational radiation give 2PN dissipative correction to the gravitational waveform phase 300 . Also in this theory, there is a quadrupole moment deformation in the BH solution valid to quadratic order in spin, 305 which gives 2PN conservative correction.…”

Light scalar field constraints from gravitational-wave observations of compact binaries

“…Recently, building on earlier work by Jacobson [36], Horbatsch and Burgess pointed out that scalar fields that vary on cosmological timescales may violate the no-hair theorem, so that even black hole-black hole binaries may produce dipolar radiation [37]. The existence of dipolar radiation in extended theories of gravity and the investigation of possible bounds on dipolar radiation are active research topics [38][39][40].…”