Graviton Mass in the Era of Multi-Messenger Astronomy

Round 1

Reviewer 1 Report

I have read the contribution entitled "GRAVITON MASS IN THE ERA OF MULTI-MESSENGER ASTRONOMY", and I think it deserves publication after a careful revision of the English language and style.

From the scientific point of view, I have few or minor comments. Everything sounds correct, and the papers to which the author refers for more details help to clarify most of the aspects which cannot be included in this proceeding for length reasons. I would probably suggest to reduce a bit the Introduction (some notions are nowadays well established) and introduce more details in the next sections to stress more clearly what are the direct contributions from the author to  the field.

Although, I strongly advice the author to take her time to revise carefully the English. Not only because of some typos and mistakes (there are many, distributed all over the text), but mostly for the style. Some sections seem to have been written in a hurry; some sentences are not well structured (it seems like the author started to think to write something and then changed her mind, without rephrasing the previous parts). This would help a lot the reading.

Kind regards,

The Referee 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

The paper is an interesting summary of the main methods to assess upper limits on the graviton mass.

I report here a couple of substantial remarks:

line 112- 116 

• <<Therefore, in this context the most attractive objects are   high-energy extra-galactic sources like active galactic nuclei (AGNs), gamma-ray bursts   (GRBs), pulsars and, recently, double compact object (DCO) mergers. These sources are promising also due to their extremely regular (pulsars, DCO mergers) or fine-scale (GRBs, AGNs) time structure required for time delay technique to be robust. >>
  The present catalog of know pulsars concerns  mainly galactic object. Thus, the mixture of pulsars  with AGN and GRB could be misleading.  In addition it is true that pulsars are emitting regular ( quasi-periodic) signals, GRBs not.In this sense it will be much more clear to discuss separately the advantage to use pulsars for deriving limits on the graviton masses from that of AGN and GRBs. In practice, I am asking to  rewrite this block of sentences by separating pulsars the case of pulsar from AGN and GRB.

line 119 

The question of the absolute value of the neutrino mass is still an open issue. In addition the neutrino flavour oscillates during its travel toward the observer, making more complicated the  assessment of its propagation time. the main focus of the review is the methods of  deriving graviton mass: up to now in the literature the attempt was to use of GW signals to derive an upper limit on the neutrino mass, not viceversa.

line 75 —  extended at line 114

My general  remark concerns the style. This is a useful review article and it is important  to release a version for a smooth and pleasant reading. Here the author follows the  modern attitude to make extensive use of acronyms, resulting  in a more heavy reading of the review article. In addition, in one case ( DOE) the extension of the acronyms is postpone several lines after its first citation. A reduction of the number od acronyms used here, will help.

line 354 -361

Section << Summary and discussion of perspectives>>

 The author emphasises the stringent bound on gravitation mass  obtained by looking at deviations in the galaxy cluster total mass (the upper limit  is  reported  even at the end of the abstract). 

However, in the section ‘Graviton mass from dynamical properties of galaxy clusters’  it is pointed out that this bound is obtained under assumptions as those  of the role of the ‘mysterious’ dark part of the inter-cluster medium, the spherical symmetry and  the state equation of perfect gas. 

In the final section  the author  is summarising the paper content in a rather elegant way, but all these considerations concerning the 10  ^{-19} eV  bound, affecting significantly the robustness of the bound, are  absent.  Here the author should   refer explicitly to the discussion reported in the previous section to frame this result in a more fair perspective. 

In the text that I have got in a pdf format there are  few  misprints.

line 14

This is the most striking one: the absence of the “minus” sign in the exponent of the upper limit  cited at line 14 of the Abstract 

present version

m_g< (4.99 - 6.79)x 10 E29 eV 

to be corrected as 

m_g< (4.99 - 6.79)x 10 E-29 eV 

line 29

misprint: bee able==> been able

lines 124-125

Friedman-Robertson-Walker model

<< ds^2 = c^2 dt^2 {a(t)}^2 [dr^2 + r^2 d^2 + r^2sin^2 d^2] >>

Please check  this formula: it is mathematically inconsistent:

- In the square parenthesis it appears  the square of a differential quantity summed to finite quantities !!! 

-   dt^2 multiplies the parenthesis so that we have an expression for  ds^2, which includes a therm  proportional to (dr^2   x dt^2)  !!!

My guess is that it is LaTeX mistyping: in  the GR literature the FRW metric in  polar coordinates is

 ds^2 = c^2 dt^2 - {a(t)}^2 [\frac{dr^2}{1-kr^2} + r^2 d\theta^2 + r^2 sin^2\theta d\varphi^2]

with k =0, \pm 1 -  representing the curvature of the space.

line 136

end of the line

formula h(z)=  …..  not fully legible 

line 201

Forecasts ==> Predictions

line 225

Add a reference at the end of <<the following:>>  to justify formula (8)

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Dear Editor,

Dear Authors,

I think that the paper is now ready for publication.

Regards,

The Referee