From 1719f067091991d9242101002af8686484380f88 Mon Sep 17 00:00:00 2001
From: Thomas Ng <thomas.ng@link.cuhk.edu.hk>
Date: Wed, 18 Oct 2023 02:15:41 +0800
Subject: [PATCH] Update ms.tex

---
 src/tex/ms.tex | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/tex/ms.tex b/src/tex/ms.tex
index f1d0279..845fc0c 100644
--- a/src/tex/ms.tex
+++ b/src/tex/ms.tex
@@ -34,7 +34,7 @@
 \begin{abstract}
     The propagation of gravitational waves can reveal fundamental features of the structure of spacetime.
     For instance, differences in the propagation of gravitational-wave polarizations would be a smoking gun for parity violations in the gravitational sector, as expected from birefringent theories like Chern-Simons gravity.
-    Here we look for evidence of amplitude birefringence in the \replaced{third gravitational-wave transient}{latest Laser Interferometer Gravitational Wave Observatory-Virgo} catalog (GWTC-3) through the use of birefringent templates inspired by dynamical Chern-Simons gravity.
+    Here we look for evidence of amplitude birefringence in the \replaced{third catalog of detections by the Laser Interferometer Gravitational Wave Observatory and Virgo}{latest Laser Interferometer Gravitational Wave Observatory-Virgo catalog (GWTC-3)} through the use of birefringent templates inspired by dynamical Chern-Simons gravity.
     From 71 binary-black-hole signals, we obtain the most precise constraints on gravitational-wave amplitude birefringence yet, measuring a birefringent attenuation of \variable{output/restricted_kappa_median.txt} at $100 \, \mathrm{Hz}$ with 90\% credibility, equivalent to a parity-violation energy scale of \variable{output/M_PV_constraint.txt}.
 \end{abstract}
 
@@ -574,7 +574,7 @@ \subsubsection{Okounkova et al.}
 On the other hand, our constraint from Sec.~\ref{sec:results:gwtc} is \variable{output/restricted_absolute_kappa_68.txt} at $100 \, \mathrm{Hz}$ at 68\% credibility.
 This is a factor of \variable{output/improvement_Okounkova.txt}more stringent than Ref.~\cite{Okounkova_2022}, besides arising from a less simplified model.
 
-The result of \citet{Okounkova_2022} is also phrased in terms of a canonical Chern-Simons length scale,\footnote{This results from setting the so-called ``canonical'' Chern-Simons embedding into an Friedmann-Robertson-Walker cosmology, where the Chern-Simons field evolves as $\theta \propto t$ \cite{Alexander:2009tp,Jackiw:2003pm,Yunes2009}.}
+The result of \citet{Okounkova_2022} is also phrased in terms of a canonical Chern-Simons length scale,\footnote{This results from setting the so-called ``canonical'' Chern-Simons embedding into a Friedmann-Robertson-Walker cosmology, where the Chern-Simons field evolves as $\theta \propto t$ \cite{Alexander:2009tp,Jackiw:2003pm,Yunes2009}.}
 \begin{equation}
     l_0 = \frac{c d_H \kappa}{3 \pi f} = 1400 \, \mathrm{km} \left( \frac{\kappa}{1 \, \mathrm{Gpc}^{-1}} \right) \left( \frac{100 \, \mathrm{Hz}}{f} \right);
 \end{equation}