Parity Violation in Spin-Precessing Binaries: Gravitational Waves from the Inspiral of Black Holes in Dynamical Chern-Simons Gravity

Abstract

Spin precession in compact binaries is intricately tuned to the multipole structure of the underlying bodies. For black holes, violations of the no-hair theorems induced by modifications to general relativity correct the precession dynamics, which in turn imprints onto the amplitude and phase modulations of the gravitational waves emitted by the binary. Recently, the spin precession equations were derived up to second order in spin for dynamical Chern-Simons gravity, a parity violating modified theory of gravity. We here solve these equations and construct, for the first time, analytic expressions for the time- and frequency-domain gravitational waves emitted in the quasi-circular inspiral of spin-precessing black hole binaries in a modified theory of gravity using the post-Newtonian approximation. Working within the small coupling approximation and using multiple scale analysis, we show that the corrections to the nutation phase enter at relative 1PN order, and the corrections to the precession angle and Thomas phase enter at relative 0PN order. Making use of the stationary phase approximation and shifted uniform asymptotics, we find that the Fourier phase of the waveform is characterized by three modifications, two due to the back-reaction of the precession dynamics onto the spin-orbit and spin-spin couplings that enter at 1.5PN and 2PN orders, and a 2PN modification due to the emission of dipole radiation. We also find that back-reaction of the precession dynamics forces the dCS corrections to the Fourier amplitude to enter at 0PN order, as opposed to 2PN order, as expected for spin-aligned binaries. Our work lays the first foundational stones to build an inspiral-merger-ringdown phenomenological model for spin-precessing binaries in a modified theory of gravity.

32 pages, 4 figures, published version

References in corpus (16)

• Effective Field Theory for Inflation
• Dynamical Chern-Simons Modified Gravity I: Spinning Black Holes in the Slow-Rotation Approximation
• Analysis of spin precession in binary black hole systems including quadrupole-monopole interaction
• The Barbero-Immirzi Parameter as a Scalar Field: K-Inflation from Loop Quantum Gravity?
• Improved gravitational-wave constraints on higher-order curvature theories of gravity
• Effective potentials and morphological transitions for binary black-hole spin precession
• Interaction of the Barbero--Immirzi Field with Matter and Pseudo-Scalar Perturbations
• Quasinormal modes of slowly-rotating black holes in dynamical Chern-Simons gravity
• The Initial Value Formulation of Dynamical Chern-Simons Gravity
• Peccei--Quinn mechanism in gravity and the nature of the Barbero--Immirzi parameter
• Bounding the mass of the graviton with gravitational waves: Effect of spin precessions in massive black hole binaries
• Canonical Formulation of Spin in General Relativity
• Fast Frequency-domain Waveforms for Spin-Precessing Binary Inspirals
• Are Parametrized Tests of General Relativity with Gravitational Waves Robust to Unknown Higher Post-Newtonian Order Effects?
• The Chern-Simons Caps for Rotating Black Holes
• Inspiralling compact objects with generic deformations