Neutron Stars in f(R)-Gravity and Its Extension with a Scalar Axion Field
Round 1
Reviewer 1 Report
This manuscript studies the impact on the properties of neutron stars of f( R ) -gravity and its extension with Scalar Axion Field. The authors discuss mass-radius relations, mass profile, the role of the central density for various equations of state and they compare the results against General Relativity.
Overall the paper is scientifically sound and worth of publication in Particles as it address an interesting topic at the intersection of the community of astrophysics, nuclear theory, particle physics and cosmology. Nevertheless there are a few points that seem to be unclear and should be revised before publication.
- In lines 29-30 the authors claim that there is no well-established data about mass-radius relation from astronomical observations. There are numerous observations that place stringent limits in the mass-radius relation. The authors could refer to Steiner et al. (Astrophysical Journal Letters, Volume 765, Issue 1, article id. L5, 5pp. 2013) and to Bogdanov et al. (The Astrophysical Journal Letters, Volume 887, Issue 1, article id. L26, 23pp. 2019) for observational that can be compared against the measured values and discuss their results in the context of these models.
- While the equations are clearly derived in section 2, it is not clear how the system of differential equations (17), (18), (19) and (22) is integrated to obtain the results presented in the figures. If the authors have done so numerically they could state the method they used.
- In the paragraph in lines 75-80 the authors state that the gravitational mass outside the conventional surface of the star is non-zero, a consequence of R^2-gravity. They could explain this effect a bit further or provide a reference, as they have stated in the top of page 7 that the surface of the star is located at e=p=0.
- In relation to point (1) the Discussion section should address whether the results are consistent with the existing observations.
There are a few typos and grammar mistakes, so I would recommend a careful proofreading prior to publication.
Author Response
Please see attachment
Author Response File: 
Author Response.docx
Reviewer 2 Report
Dear editor(s)
the authors present present a review of some of their recent results on
nonrotating neutron star solution in R^2-gravity. I think that in overall the
summary is well-presented and fits within the context of the special issue.
I do recommend it for publication, but I do have comments and questions on the
manuscript which are list below. I would greatly appreciate if the authors
could address them.
***
1. p1, line 28: I would recommend citing the original references for the two
equations of state used (GM1 and APR). Also, although understood, the acronym
EoS is not defined. I would suggest saying 'two equations of state (EoS)' in
this line.
2. p1, lines 29-30: Of course the authors are correct about the lack of precise
data to determine the neutron star mass-radius diagram. However, this scenario
is changing, for instance with the observations made by NICER and with
gravitational wave observations. Maybe the authors could add a sentence to this
paragraph mentioning this and citing a few relevant literature, say, for
instance:
https://inspirehep.net/literature/1770430
https://inspirehep.net/literature/1772243
3. p2, above Eq. (4): I think the authors meant that 'One can rewrite (3)' (and
not (2)).
4. p3, above Eq. (14): I would recommend saying 'the trace of the first
equation (7)' to help the reader follow, as the 'first equation' is seven
numbered equation back.
5. p3, below Eq. (20): I am confused with the terminology 'physical radial
coordinate'. $\tilde{r}$ is the circunferential radius, which perhaps it is a
better name. But of course, I will not push into the authors.
6. p4, line 43. The authors could cite
https://inspirehep.net/literature/1341964
https://inspirehep.net/literature/1625242
as well.
7. p5, below Eq. (21): Is there any particular reason for the choice of the
'simple form' for the interaction between $phi$ and $R$ to involve $R^2$? The
simplest choice would arguably be $phi R$, i.e. a standard nonminimal coupling.
I would appreciate if the authors can explain / justify their choice in the
manuscript.
8. p7. equation below Fig. 4: This equation contains a third derivative of $f$
with respect to $R$, while page 2, it is said that only the first and second
derivatives need to exist for f. This probably warrant a comment or a
correction to the text.
9. figures and table 1: the authors use $r_g$ for the units, but I don't believe
that it is defined in the text (although it look reasonable to assume that it
stands for the gravitational radius).
10. p 7, line 76: Their discussion on the mass is an interesting feature of
stellar solutions in this theory. Have the authors considered the role of this
effect on geodesic motion around the star? This could be interesting
astrophysically. Similar studies in the context of scalar-tensor theory
include:
https://inspirehep.net/literature/1391114
that are maybe worth mentioning.
On the same topic, in Fig. 2, I would recommend the authors to normalize
the x-axis by the radius of the star, such that it is easier to the reader
to understand where the vacuum region around the star is. I would recommend
the same for Figs. 3 and 4.
11. p8, final paragraph: the authors are absolute right regarding the lack of
precise mass-radius measurements and uncertainties on the equation of state
(which could be called 'EoS' here, since the acronym has been introduced).
It would be good to point out that one can still derive equation-of-state
independent relations for neutron star properties, which can then be used to
test the theory of gravity. For a review see:
https://inspirehep.net/literature/1480157
And for an recent application to test deviation to general relativity see
https://inspirehep.net/literature/1789587
In principle, if the authors were to work out the I-Love relation in $R^2$
theory, the same idea of the paper above can be applied and then a bound can be
places on the theory (if the observation are to be consistent with general
relativity).
Of course, I do ask this to be done in this manuscript, but it is just an idea
that I am throwing out and that the authors may find interesting to pursue.
Author Response
Please see attachment
Author Response File: Author Response.docx
