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

Nicholas Loutrel, Nicolás Yunes|arXiv (Cornell University)|May 5, 2022

Pulsars and Gravitational Waves ResearchPhysics and Astronomy79 references23 citations

TL;DR

This paper derives the first analytic time- and frequency-domain gravitational waveforms for spin-precessing black hole binaries in dynamical Chern-Simons (dCS) gravity using post-Newtonian theory. It shows that dCS corrections enter the Fourier domain waveform phase at 0PN, 1.5PN, and 2PN orders due to precession back-reaction and dipole radiation, with amplitude corrections at 0PN—marking a key departure from spin-aligned binaries and enabling new tests of parity-violating 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.

Motivation & Objective

• To construct the first analytic time- and frequency-domain gravitational waveforms for spin-precessing black hole binaries in dynamical Chern-Simons (dCS) gravity.
• To extend post-Newtonian theory to include dCS corrections in the spin precession dynamics and waveform evolution.
• To determine the order at which dCS corrections enter the Fourier domain waveform phase and amplitude, accounting for precession back-reaction.
• To establish foundational tools for building full inspiral-merger-ringdown models in modified gravity theories with spin precession.

Proposed method

• Solving the spin precession equations in dCS gravity up to second order in spin using multiple scale analysis within the small coupling approximation.
• Constructing a co-precessing reference frame analogous to GR, preserving integrability via the mass-weighted effective spin.
• Applying the stationary phase approximation and shifted uniform asymptotics to derive the Fourier-domain waveform from the time-domain signal.
• Identifying the leading-order corrections to the waveform phase from dCS: 1.5PN from spin-orbit coupling, 2PN from spin-spin coupling, and 2PN from dipole radiation.
• Computing amplitude corrections by accounting for precession back-reaction, showing they enter at 0PN order rather than 2PN as in spin-aligned cases.
• Using effective field theory methods to derive dCS-modified spin-orbit, spin-spin, and monopole-quadrupole interactions in the PN expansion.

Experimental results

Research questions

• RQ1 At what post-Newtonian order do dCS gravity corrections enter the Fourier domain phase of gravitational waveforms from spin-precessing binaries?
• RQ2 How does the back-reaction of precession dynamics modify the amplitude corrections in dCS gravity compared to standard GR or spin-aligned binaries?
• RQ3 What is the relative order of magnitude of dCS corrections to the nutation phase, precession angle, and Thomas phase in the PN expansion?
• RQ4 Can the dipole radiation emission in dCS gravity be distinguished from spin-induced effects in the Fourier domain through waveform modeling?
• RQ5 How do the dCS corrections to the precession dynamics affect the structure of the inspiral waveform in the frequency domain?

Key findings

• The dCS correction to the nutation phase enters at relative 1PN order, while corrections to the precession angle and Thomas phase enter at relative 0PN order.
• The Fourier domain waveform phase is modified by three distinct dCS effects: 1.5PN from spin-orbit back-reaction, 2PN from spin-spin back-reaction, and 2PN from dipole radiation.
• The amplitude correction due to dCS gravity enters at 0PN order due to precession back-reaction, contrary to the 2PN order expected in spin-aligned binaries.
• The dCS corrections to the waveform are not degenerate with spin effects in precessing systems, offering a potential pathway to break degeneracies in parameter estimation.
• The work establishes the first analytic framework for building full inspiral-merger-ringdown models in dCS gravity for spin-precessing binaries.
• The results imply that spin-precessing binaries in dCS gravity can provide stronger constraints on the dCS coupling constant than spin-aligned systems, due to enhanced signal structure.