Editorial suggestions for JOSS paper

paper/paper.md

@@ -54,13 +54,13 @@ The following brief overview has been prepared as part of the submission of the
 
 # Summary
 
-Gravitational waves (GWs) are generated by the mergers of dense, compact objects like black holes (BHs) and neutron stars (NSs). This provides an opportunity to study the strong field, highly dynamical regime of Einstein's theory of general relativity (GR) at higher curvature scales than previous observations [@LISA:2022kgy;@Perkins:2020tra;@Barausse:2020rsu;@Gnocchi:2019jzp;@Barack:2018yly;@Baker:2014zba]. It is possible that at such scales modifications to GR may start manifest. However, in order to detect such modifications, we need to understand what deviations could look like in theories beyond GR, in particular in the merger section of the signal in near equal mass binaries, which are key targets of the LIGO-Virgo-KAGRA network of detectors (and their future 3G successors). Such predictions necessitate the use of numerical relativity (NR), in which the (modified) equations of GR are evolved from an initial configuration several orbits before merger, through the merger period and the subsequent "ringdown", during which the gravitational wave signal can be extracted near the computational boundary.
+Gravitational waves (GWs) are generated by the mergers of dense, compact objects like black holes (BHs) and neutron stars (NSs). This provides an opportunity to study the strong field, highly dynamical regime of Einstein's theory of general relativity (GR) at higher curvature scales than previous observations [@LISA:2022kgy;@Perkins:2020tra;@Barausse:2020rsu;@Gnocchi:2019jzp;@Barack:2018yly;@Baker:2014zba]. It is possible that at such scales modifications to GR may start to manifest. However, in order to detect such modifications, we need to understand what deviations could look like in theories beyond GR, in particular in the merger section of the signal in near equal mass binaries, which are key targets of the LIGO-Virgo-KAGRA network of detectors (and their future 3G successors). Such predictions necessitate the use of numerical relativity (NR), in which the (modified) equations of GR are evolved from an initial configuration several orbits before merger, through the merger period and the subsequent "ringdown", during which the gravitational wave signal can be extracted near the computational boundary.
 
 Current waveforms are tested for consistency with GR by measuring parameterised deviations to the merger, inspiral and ringdown phases [@Maggio:2022hre;@Krishnendu:2021fga;@LIGOScientific:2021sio;@Carson:2019kkh;@Cornish:2011ys], and not by comparison to any particular theories. If we obtain predictions for specific models, we can check whether such parameterised deviations are well-motivated and consistent in alternative theories of gravity [@LISA:2022kgy;@Okounkova:2022grv;@Johnson-McDaniel:2021yge;@Shiralilou:2021mfl;@Perkins:2021mhb;@Carson:2020ter;@Carson:2020cqb], and the potential to extract model parameters from data.
 
 There are many ways to modify GR, one of the simplest being to couple an additional scalar degree of freedom, which may (if certain conditions are satisfied) result in so-called "hairy" stationary black hole solutions; that is, black holes with a stable, non trivial configuration of the scalar field around them (see [@Doneva:2022ewd] for a review). An example of this is the class of Horndeski models [@Horndeski:1974wa]. Cubic Horndeski theories have been studied in [@Figueras:2020dzx,@Figueras:2021abd] and an implementation of this is included in GRFolres. Another more general example within the Horndeski models is the four-derivative scalar-tensor theory ($4\partial$ST), which is the most general theory with up to fourth powers of the derivatives (but still second order equations of motion). Despite their relative simplicity, they have lacked well-posed (and thus numerically stable) formulations until relatively recently.
 
-An important breakthrough was made in 2020 by Kov\'acs and Reall, who showed that Horndeski theories are indeed well-posed in a modified version of the harmonic gauge [@Kovacs:2020pns;@Kovacs:2020ywu] -- a particular coordinate system already used in NR. Subsequently, several specific theories within these classes were probed in their highly dynamical and fully non-linear regimes [@East:2020hgw;@East:2021bqk;@East:2022rqi;@Corman:2022xqg]. The extension of the results of [@Kovacs:2020pns;@Kovacs:2020ywu] to the alternative "singularity avoiding" coordinates in [@AresteSalo:2022hua;@AresteSalo:2023mmd;@Doneva:2023oww] offers an alternative gauge in which to probe questions of hyperbolicity, and may offer stability advantages for certain cases such as unequal mass ratios, as studied in [@Corman:2022xqg]. Numerical work on these theories is still in the early stages of development and many technical details on their numerical implementation need to be further investigated. Equally, many scientific questions, concerning our accurate understanding of binary black holes' phenomenology in alternative theories of gravity and their implications for tests of GR, also remain unanswered.
+An important breakthrough was made in 2020 by Kov\'acs and Reall, who showed that Horndeski theories are indeed well-posed in a modified version of the harmonic gauge [@Kovacs:2020pns;@Kovacs:2020ywu] -- a particular coordinate system already used in NR. Subsequently, several specific theories within these classes were probed in their highly dynamical and fully non-linear regimes [@East:2020hgw;@East:2021bqk;@East:2022rqi;@Corman:2022xqg]. The extension of the results of [@Kovacs:2020pns;@Kovacs:2020ywu] to the alternative "singularity avoiding" coordinates in [@AresteSalo:2022hua;@AresteSalo:2023mmd;@Doneva:2023oww] offers an alternative gauge in which to probe questions of hyperbolicity, and may offer stability advantages for certain cases such as unequal mass ratios, as studied in [@Corman:2022xqg]. Numerical work on these theories is still in the early stages of development and many technical details on their numerical implementation need to be further investigated. Equally, many scientific questions, concerning our accurate understanding of binary—black-hole phenomenology in alternative theories of gravity and their implications for tests of GR, also remain unanswered.
 
 The goal of GRFolres is to meet this need for further research, and to provide a model code to help others develop and test their own implementations. The code is based on the publicly available NR code GRChombo [@Clough:2015sqa;@Andrade:2020dgc], which itself uses the open source Chombo framework [@Adams:2015kgr] for solving partial differential equations (PDEs).
 
@@ -72,7 +72,7 @@ GRFolres inherits many of the features of GRChombo and Chombo. Here we list the
 
 - Stable gauge evolution - The code implements the modified moving puncture gauge that ensures a well-posed evolution in the weak coupling regime, as proposed in [@AresteSalo:2022hua]. The precise form of the gauge and its parameters can be changed and the standard moving puncture gauge is safely recovered by setting certain parameters to zero.
 
-- Modified gravity theories - The currently available theories in the code are 4∂ST and cubic Horndeski. The code is templated over the theory (in the same way that GRChombo is templated over a matter class) so that it can easily be changed without major code modifications. The code also provides an implementation of 4∂ST without backreaction onto the metric (but including the possibility of using the new gauge), to enable comparison with previous works using the decoupling limit approximation.
+- Modified gravity theories - The currently available theories in the code are 4$\partial$ST and cubic Horndeski. The code is templated over the theory (in the same way that GRChombo is templated over a matter class) so that it can easily be changed without major code modifications. The code also provides an implementation of 4$\partial$ST without backreaction onto the metric (but including the possibility of using the new gauge), to enable comparison with previous works using the decoupling limit approximation.
 
 - Accuracy - The fields are evolved with a 4th order Runge-Kutta time integration and their derivatives calculated with the same finite difference stencils used in GRChombo (4th and 6th order are currently available).
 
@@ -114,17 +114,17 @@ So far the code has been used to study a range of fundamental physics problems,
 ![Energy density (in blue) of the scalar field surrounding the binary black holes for the Horndeski theory at a representative instant of time during the inspiral phase. The apparent horizon of the black holes is shown in orange. The region where the weak coupling conditions are larger than one is depicted in brown. Taken from [@Figueras:2021abd].\label{fig:cubic}](Figures/EnergyDensity_and_WFC.png){width=95%}
 
 
-- In the work [@AresteSalo:2022hua], the code was developed and tested, with waveforms for shift-symmetric theories of Einstein-scalar-Gauss-Bonnet gravity produced for equal mass binaries.
+- In [@AresteSalo:2022hua], the code was developed and tested, with waveforms for shift-symmetric theories of Einstein-scalar-Gauss-Bonnet gravity produced for equal mass binaries.
 
 ![Modified gravity waveforms in $4\partial$ST with a shift-symmetric coupling. Taken from [@AresteSalo:2022hua].\label{fig:waveform}](Figures/all_waves.png){width=95%}
 
 
-- In the work [@AresteSalo:2023mmd], the studies were extended to binary mergers in theories with spin-induced scalarisation. The clouds formed are dumbbell-like in shape.
+- In [@AresteSalo:2023mmd], the studies were extended to binary mergers in theories with spin-induced scalarisation. The clouds formed are dumbbell-like in shape.
 
 ![The time evolution of the density of the scalar cloud that develops in Einstein-scalar-Gauss-Bonnet gravity with an exponential coupling, resulting in spin-induced scalarisation. Taken from [@AresteSalo:2023mmd].\label{fig:spin}](Figures/rhophi.png){width=95%} 
 
 
-- In the work [@Doneva:2023oww], the dependence of the conditions for hyperbolicity and weak coupling were studied for spin-induced scalarisation, and the critical thresholds found for a number of cases.
+- In [@Doneva:2023oww], the dependence of the conditions for hyperbolicity and weak coupling were studied for spin-induced scalarisation, and the critical thresholds found for a number of cases.
 
 ![The time evolution of the determinant of the effective metric in a case of spin-induced scalarisation. When the determinant is negative (in black) outside the apparent horizon (depicted with a dashed white line), the theory has become ill-posed. Taken from [@Doneva:2023oww].\label{fig:hyperbolicity}](Figures/discriminant_beta200.png){width=95%}