Dark Coincidences: Small-Scale Solutions with Refracted Gravity and MOND

Round 1

Reviewer 1 Report

This review deals with some challenges faced by the concordance cosmological model (LCDM) while applied to the description of galactic scale astrophysics. The paper focus on three relations (the BTFR, MDAR and RAR relations) which are particular unnatural to explain by LCDM model. It is show that two modified gravity frameworks are capable of predicting the aforementioned relations, namely MOND and Refracted Gravity. The manuscript is comprehensive, it is clearly written and contains a good number of references for a review paper. It was a pleasure for me to read this manuscript. Even in this case, I would suggest a careful proofreading to eliminate some persistent typos, misuse of pronouns and articles, and sentences unnecessarily long; specifically, the second paragraph of page 20 is particularly confusing. (Moreover, the use of the word  "although" in the Conclusion sounds inadequate in several places.) I do recommend this manuscript for publication is the current form.

Author Response

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Reviewer 2 Report

The manuscript considers the difference of modified Newtonian gravity and refracted gravity in explaining the origin of the dark matter. This subject is interesting. I think this idea as opposite to the other models can be proposed to folk and discussed widely.

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Reviewer 3 Report

The work "Dark coincidences: small-scale solutions with Refracted Gravity and MOND" of V. Cesare is a review on certain scale relations in galaxies and their possible connection with modified gravity, MOND and Refracted Gravity (RG). I understand that the main novelty of this review is to do a systematical analysis of RG gravity in contrast with observations and MOND. Without RG gravity, this work would loose considerably its relevance.

One of the main points of the paper is that it considers three different observations (RAR, MDAR and the BTFR) as  a confirmation for modified gravity. It is also stressed that all of them yield the same value for the constant $a_0$. I don't understand why the author follows this approach, since RAR and MDAR are essentially the same thing (as Milgrom himself has already stated, arXiv 1609.06642). BTFR is different, but it is clearly related (arXiv 1610.08981). There should be no surprise that these relations yield similar answers. Clusters, on the other hand, lead to a quite different picture. I understand that it should be clear in the paper that these tests are not independent tests that happen to find similar results. For instance, among other passages, see the sentence in the conclusions "Even more surprisingly, they all see the appearance of the same acceleration..." I ask the author to improve the presentation of such issues. 

There is a series of papers that analyse the relation between MOND, LCDM and the RAR that the author neglects (sometimes the reference is cited, but it is not commented considering the context stressed below).  She can in the end favour MOND, if she finds this right, but she should comment on these other papers in order to clarify the debate in the literature. In particular, I ask the author to comment of the following papers from different groups (for simplicity, the references are from arXiv):

1610.07663 - This paper is cited, but the interpretation of the RAR from LCDM is not explained (at least I have not seen it in the paper). I am not saying that the agreement with LCDM is without issues, but that there are simple explanations from LCDM for the RAR existence.

1806.06803, 2002.03946 -- Show that the expected a0 values from different galaxies are not compatible among themselves.

2008.04065 -- Related with the above

1906.07823 -- Other MOND criticism based on the rotation curve data

1908.06105 - Shows that the RAR scatter is compatible with LCDM.

There is some confusion in the paper considering the value of the RAR scatter. The observational RAR scatter has a dispersion of 0.1 dex (McGaugh et al 2016). In the paper of Li et al 2018, MOND was assumed to be true and the observational errors were fitted. The fact that the scatter is reduced in this picture is not model independent: the observational errors are being used to reduce the scatter. It is pointless to compare other modes with the scatter found when MOND is assumed. Less scatter does not mean that it is closer to the truth, scatter can be reduced due to unrealistic assumptions as well.  There are some sentences in the paper that need revision due to this improper comparison.

At last, this is not essential, but I suggest the author to reflect  on the repeated statement about the number 1.2 \times 10^{-10} m/s^2. Could she comment on the uncertainty of this? I note that changing the \mu function changes this expected value (several papers show this). Also I note that in many papers the quoted uncertainty is the uncertainty on the average (either the mean or the median), not the confidence interval.

This is an interesting review that may be helpful for several researchers that work on dark matter or modified gravity. However, some comments need to be revised, as above suggested.

Author Response

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Reviewer 4 Report

The author studies the structure of the Universe by using some cosmological models in some modified gravity theories. The author explains these theories, including its advantages over the $\Lambda$ cold dark matter model. Then the author focuses on the covariant refracted gravity theory and shows that the theory describes the dynamics of the galaxies and the clusters without introducing some dark components. I find this review interesting but I recommend the author to consider the following points:

i) There is no modified theory (VI) in the page 17. If exists, the author may add this. Moreover, the author may explain these theories (I)-(IX) in more detail, including its advantages in the associated cosmological models.

ii) The author may add the following papers and discuss in detail the difference between the covariant refracted gravity theory and the scalar-tensor-vector gravity one in the dark matter and the dark energy phenomenology:
[1] J. W. Moffat, V. T. Toth, arXiv:0708.1935 [astro-ph].
[2] J. R. Brownstein, J. W. Moffat, arXiv:astro-ph/0506370.
[3] J. W. Moffat, V. T. Toth, arXiv:0712.1796 [gr-qc].
[4] J. R. Brownstein, J. W. Moffat, arXiv:astro-ph/0507222.
[5] J. W. Moffat, V. T. Toth, arXiv:0710.0364 [astro-ph].

Author Response

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Round 2

Reviewer 3 Report

In this second version, the paper has significantly improved. I understand that now the paper is almost ready to be accepted. However, there are still a couple  of wrong statements that I ask the author to correct (or to explain them further, if she thinks the statements are somehow correct):

 

- I think that the author understands that MDAR, RAR and the BTFR are not independent relations. Hence, the statement in the abstract "An even more outstanding coincidence is the emergence of the same acceleration scale, (...), from all three relations, (...)" should be corrected.  MDAR is the RAR with a different pair of axes. And BTFR is also related with the previous ones, as I previously pointed out, and I think the author agrees. I suggest to remove this sentence from the abstract and to rewrite this part. There is no "outstanding coincidence", as far as these are not independent relations.

 

- Below eq. (3): "... and the systematic contributions..." This statement is too loosely used here, thus prone to misinterpretations, since this systematic uncertainty has a very specific origin.  Namely, according with ref. [22], "the systematic uncertainty represents the 20% normalization uncertainty in \Upsilon_*". I suggest to insert this short explanation (or something similar).

 

- In the next paragraph, there is the following statement: "This value is consistent with the scatter of 0.12 dex due to the observational errors..." and that "This result is confirmed by Li and collaborators [51] that found a scatter of 0.057 dex, which sets an upper limit for the RAR intrinsic scatter..." There are a couple of issues here:

--- If MOND is not being assumed, one should not use the word "consistent", but "closely coincides" or something similar. If these values were not similar, there would be no inconsistence (but it would be a problem for MOND).

--- I don't see how [51] confirms the previous result. I think the link between these works is either wrong or some clarification should be inserted. [51] uses a strong hypothesis that was not used in [22]: that the RAR observed in the sample of galaxies is true for individual galaxies. 

--- Since [51] assumes that the RAR is valid for individual galaxies, which is a model closely related to MOND, it cannot find a model-independent upper limit on the RAR intrinsic scatter. 

 

- In the paragraph that starts with "It should be pointed out that some studies question the MDAR and the RAR..." I know of no works that question the RAR or MDAR existence, and [54] is not an example for that. There is no doubt that one can assume eq. (3) and, from a sample of galaxies, find the best fit for g_\dagger. The resulting scatter about the eq.(3) curve is clearly small, as shown by [22]. What is not trivial is to ask if eq. (3) has a more fundamental origin and if it is true for all the individual galaxies. To test this, one can infer g_\dagger for each galaxy and compare the results, the marginalized g_\dagger posteriors, to see if the individual results are compatible among themselves, as done by [54, 56]. Ref. [51] does not compare the g_\dagger posteriors and it does not quantify the probability. The other references [58, 59] were properly cited. I ask the author to carefully rewrite this part, either following these suggestions or explaining it better.

 

Author Response

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Reviewer 4 Report

I am satisfied with the corrections by the author.
Then I recommend the publication of this work.

Author Response

I thank very much the referee for her/his comment and recommendation.