The Scale-Invariant Vacuum Paradigm: Main Results and Current Progress Review (Part II)†
Round 1
Reviewer 1 Report (New Reviewer)
Comments and Suggestions for AuthorsThe present manuscript is the second part of a review on the Scale
Invariant Vaccum (SIV) paradigm, based on Weyl's integrable geometry.
The manuscript is well-structured and seems to have been written with care.
As a review article, I believe that it is of great interest to researchers
in the field, as it complements previous published works of the same
authors on the theme. ["The Scale Invariant Vacuum Paradigm: Main Results
and Current Progress". Universe 2022, 8, 213.]
For the aforementioned reasons, I recommend its publication in the present form.
Author Response
We are grateful to the reviewer for taking the time to review our manuscript and highly appreciate the reviewer’s familiarity with our research.
Reviewer 2 Report (New Reviewer)
Comments and Suggestions for AuthorsThis manuscript as the second part of a review on the Scale Invariant Vacuum (SIV) paradigm based on the Weyl Integrable Geometry focuses on its application to cosmology. For early universe, it discussed the inflation scenario, Big Bang, Nucleosynthesis as well as the density fluctuations within the SIV. For late time universe, it discussed the scale-invariant dynamics of galaxies, MOND, dark matter as well as the dwarf spheroidals, and it is argued that MOND is a peculiar case of the SIV theory. Before recommending this manuscript for publication in Symmetry, I have the following questions and comments that should be answered or clarified:
1.The abstract should be improved to manifestly state what are the main results when SIV is applied to the early universe.
2.How is the scalar field $\lambda$ specified in different circumstances? In cosmological setup, it is clearly shown in Eq.(20), (25), (26). What is its behavior when applying to the Galaxy and MOND in section from 3.2 to 3.5? Usually in standard cosmology, dark energy or the cosmological constant is responsible for the acclerated expansion of the universe,while dark matter is responsible for the modified of Newton gravity. If one intends to explain all these things with one single field, one must require this field must exhibit distinct behavior in different circumstances. It is not clear how the authors do this in this review. If it is true that the scalar field exhibit different behavior, what is the mechanism leading to these changes?
Comments on the Quality of English Language
The abstract should be improved to manifestly state what are the main results when SIV is applied to the early universe.
Author Response
We are grateful to the reviewer for this wonderful suggestion.
1.The abstract should be improved to manifestly state what are the main results when SIV is applied to the early universe.
Answer: The text added to the abstract is in blue.
2.How is the scalar field $\lambda$ specified in different circumstances? In cosmological setup, it is clearly shown in Eq.(20), (25), (26). What is its behavior when applying to the Galaxy and MOND in section from 3.2 to 3.5? Usually in standard cosmology, dark energy or the cosmological constant is responsible for the accelerated expansion of the universe, while dark matter is responsible for the modified of Newton gravity. If one intends to explain all these things with one single field, one must require this field must exhibit distinct behavior in different circumstances. It is not clear how the authors do this in this review. If it is true that the scalar field exhibit different behavior, what is the mechanism leading to these changes?
Answer: This is a very good set of questions that we are still pondering over. So, we don’t want to speculate too much since the scalar field \lambda seems to be quite different from the usual type of fields one deals within physics. However, we can disclose that we have recently submitted a paper for peer review that is discussing the values of the Einstein cosmological constant and the MOND acceleration a0 as evaluated within the SIV framework. We can only state that the corresponding values do have the correct orders of magnitudes upon utilization of the reasonable cosmological parameters like Omega_m and age of the universe. Ideally one would like to have all the relevant parameters to be fitted as it is done in the LCDM, hopefully such studies will provide more information on how one should specify the scalar field \lambda in different circumstances.
Reviewer 3 Report (New Reviewer)
Comments and Suggestions for AuthorsIn the submitted manuscript, a review on several astrophysical and cosmological aspects of the SIV paradigm is given. I feel that it would be useful to people working on diverse areas and disciplines. Before I make my final decision, I ask the authors to address the following issues:
1. In one of the figures there is time on the x axis without units. Is it dimensionless, like Ho t for instance? Please clarify.
2. In the captions the numerical value of the parameter lambda is not specified, neither the value of the wavenumber k when discussing the evolution of perturbations. Please specify.
3. What about the combinatiin parameter A=f sigma versus redshift? How does it compare to current data and to the LCDM model?
4. Finally, I am sure that the interested reader wants to know weather or not there is a value of lambda for which the predictions of the paradigm agree with all the data discussed in the review.
Therefore I am asking for minor revisions.
Author Response
In the submitted manuscript, a review on several astrophysical and cosmological aspects of the SIV paradigm is given. I feel that it would be useful to people working on diverse areas and disciplines. Before I make my final decision, I ask the authors to address the following issues:
We are grateful to the reviewers for taking the time to review our manuscript and highly appreciate the reviewer’s comments and suggestions. Our answers are below as well as in blue color within the text of the new manuscript.
1. In one of the figures there is time on the x axis without units. Is it dimensionless, like Ho t for instance? Please clarify.
We have added a clarification to the Fig.1 caption.
2. In the captions the numerical value of the parameter lambda is not specified, neither the value of the wavenumber k when discussing the evolution of perturbations. Please specify.
In the SIV there is no new parameters and the lambda is usually given by eq. (15) with the appropriate attention to units utilized for the specific applications. While the related parameter kappa is given by (1) or (26). The two figures relevant for the Density Fluctuations are Fig. 6 and 7 but there is no wavenumber k there, but a symbol n defined in (41) and in the footnote on the same page 19.
3. What about the combinatiin parameter A=f sigma versus redshift? How does it compare to current data and to the LCDM model?
We are sorry, but the question above is unclear to both of us.
4. Finally, I am sure that the interested reader wants to know weather or not there is a value of lambda for which the predictions of the paradigm agree with all the data discussed in the review.
We explained the functional form of lambda in our answer to Q2 above. The scale factor λ is according to the gauging condition (t_0=1) equal to 1/t. Now, the relation of t with the value of τ0 ( in years or seconds) depends according to Eq. (22) on Ωm. The various tests performed generally favor a low value of this parameter which lets little or no room for dark matter.
Reviewer 4 Report (New Reviewer)
Comments and Suggestions for AuthorsIn this review, a current summary of a special proposal, called the scale invariant vacuum paradigm by the present authors, is presented. This specific paradigm is applied to all the important subjects of modern cosmology such as inflation in the early universe, Big Bang Nucleosynthesis, dark matter, dark energy, even the standard framework of modern cosmology of the \Lambda CDM model.
It is respected that the manuscript is presented in detail and the organization seems to be appropriate enough.
However, there are several crucial concerns.
(i)This review mainly focus on the past works by the present authors (Refs. [1--1]) and other related important references in the literature are not explained in detail enough. (Such a review might be accepted for only the case of an invited review by Editor. This seems to be a kind of digest version of the sequential works by the present authors in the literature. Even for such a case, other results and references on the corresponding subjects should be described as an original review paper.) The scope of the cosmological subjects are also too broad because all issues of modern cosmology are related.
(ii)The scale invariant vacuum paradigm is a very special one and seems not to be established yet, compared with the \Lambda CDM model. There are discussions and arguments for the paradigm itself, namely, whether the proposed theory itself is appropriate or not as a fundamental theory of gravitation.
(iii)It is stated that MOND is a peculiar case of the present paradigm, but the references listed in MOND and the detailed comparison are not to be enough. (iv)This is a kind of a sequel of the first review Ref. [9] by the present authors. Therefore, this second review should be submitted to the same journal of Ref. [9].
From the above points, in the light of the standard for publication, I am very afraid, it seems it is not suitable for publication as a review paper.
Author Response
In this review, a current summary of a special proposal, called the scale invariant vacuum paradigm by the present authors, is presented. This specific paradigm is applied to all the important subjects of modern cosmology such as inflation in the early universe, Big Bang Nucleosynthesis, dark matter, dark energy, even the standard framework of modern cosmology of the \Lambda CDM model.
It is respected that the manuscript is presented in detail and the organization seems to be appropriate enough.
However, there are several crucial concerns.
We are grateful to the reviewers for taking the time to review our manuscript and highly appreciate the reviewer’s comments and suggestions. Our answers are in blue below as well as in the text of the new manuscript.
(i)This review mainly focus on the past works by the present authors (Refs. [1--1]) and other related important references in the literature are not explained in detail enough. (Such a review might be accepted for only the case of an invited review by Editor. This seems to be a kind of digest version of the sequential works by the present authors in the literature. Even for such a case, other results and references on the corresponding subjects should be described as an original review paper.) The scope of the cosmological subjects are also too broad because all issues of modern cosmology are related.
We have added a new text on page 5 in the section 2. Mathematical Framework that should make it clear why other papers with unreasonable ideas are not included. While the text explaining the origin of (Part II) as a footnote in the title should help more with the question about the scope of the manuscript.
(ii)The scale invariant vacuum paradigm is a very special one and seems not to be established yet, compared with the \Lambda CDM model. There are discussions and arguments for the paradigm itself, namely, whether the proposed theory itself is appropriate or not as a fundamental theory of gravitation.
The point raised by the referee is a central one. One of the objectives of Science is not only to confirm epsilon-effects in existing theories, but also to explore possible new ways of thinking. This is precisely the aim of these two papers. Thus, in Paper I on the action principle, we studied and demonstrated the solid theoretical foundations of the SIV theory, also showing that our chosen gauging condition is in fact demanded by the action principle, while in this Paper II we show the convergence of various very different cosmological and local tests, locally such as the Moon recession. The exploration is on the right way, but we also emphasize the need to pursue it with other major tests.
(iii)It is stated that MOND is a peculiar case of the present paradigm, but the references listed in MOND and the detailed comparison are not to be enough.
In fact, there are many developments of MOND, QMOND, BIMOND, generalized aether theories, TRIMOND, TeVes, etc in attempt to account for different properties and to generalize it. The main point we wanted to emphasize is that the SIV rests on a unique and well defined basis see our added text to the beginning of section 3.4 on page 16.
(iv)This is a kind of a sequel of the first review Ref. [9] by the present authors. Therefore, this second review should be submitted to the same journal of Ref. [9].
We have added some text explaining the origin of (Part II) as a footnote in the title and also in the introduction. In this respect the current paper is better suited in the current second part of the Spacial Issue “Nature and Origin of Dark Matter and Dark Energy”.
Round 2
Reviewer 2 Report (New Reviewer)
Comments and Suggestions for AuthorsSome of my questions are clarified and the manuscript has been improved. I recommend it for publication.
Reviewer 4 Report (New Reviewer)
Comments and Suggestions for AuthorsThe authors' answers and revision are appreciated. The points in the review report have been considered. The revised manuscript could be suitable for publication.
This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsDear editor and authors,
The manuscript on the scale-invariant vacuum (SIV) paradigm by Gueorguiev & Maeder reviews some aspects of SIV. I have some serious concerns with the manuscript which must be addressed before it can be considered for publication.
In Section 3.1, the authors should clarify how old the universe is in their model. Observations imply an age of at least 13.5 Gyr:
https://doi.org/10.3847/1538-4357/ace439
Figure 1 of the present manuscript indicates that the universe would be somewhat younger than in LCDM. The authors must comment on this issue, ideally in section 3. The predicted age of the universe in Gyr should be stated for standard values of H_0 and Omega_M. The universe can be made older in SIV with lower Omega_M, but then the authors should clarify why that is reasonable.
In Section 3.3 and Figure 5, the authors claim that the RAR is well fit in SIV at the low-acceleration end. However, the weak lensing radial acceleration relation clearly demonstrates that the classical MOND expectation works at low accelerations:
https://arxiv.org/abs/2106.11677
There is no hint of a flattening to the relation, disproving the notion that g is asymptotically flat with respect to g_N at very low g_N, even though that is predicted in SIV. The authors must comment on this issue. The apparent flattening in the dwarf galaxy data is thought to be due to poor measurements and the impact of tides.
In Section 4, the authors should provide some curves showing the dependence of a_0 on redshift z for different Omega_M values today (note that this requires solving Eq. 35 at past epochs, when the matter density was presumably a higher fraction of the critical density than today). This may be helpful in the future as rotation curve studies at high redshift can sometimes constrain the value of a_0 then, and this is more likely as the observations improve.
In Section 3.5, the authors must address the very serious concerns raised in this publication:
https://arxiv.org/abs/2007.00654
This study appears to completely disprove the SIV paradigm using multiple interlocking lines of evidence. In particular, the authors must address measurements of the angular deceleration rate of the Moon as its orbital angular frequency decreases over time due to lunar recession. In the above paper, it was argued that these observations falsify SIV at 200 sigma confidence. The present manuscript does not provide any explanation of how this serious issue is addressed, and does not even cite the above paper at all. It must be cited in any revised version of the manuscript for it to be suitable for publication. Concerns were also raised regarding the increase in the Sun-Saturn distance over time for similar reasons to the Earth-Moon distance. Consistency with the Cassini radio tracking measurements from Saturn orbit should be discussed. In addition, the papers by Tsamis & Woodard (1986) and Jackiw & Pi (2015) cited in the above paper must be discussed as these appear to completely undermine the theoretical basis for the SIV paradigm. The authors should also comment on what their model implies for stellar evolution, since it seems to imply a much lower value for G in the past.
In light of these very serious issues, the conclusions should not be so positive for the SIV model. Instead, the conclusions should admit that SIV faces serious difficulties and that further work is required to assess if the model is viable, but it may well turn out that it is not viable.
Minor comments:
The authors should abbreviate General Relativity as GR rather than EGR, as most other workers do.
In Figure 3, the thin and thick red lines for different Omega_M are barely distinguishable. I recommend using solid and dotted red lines to distinguish between these cases.
In Figure 7, the legend indicates that the Omega_M = 0.3 case is in blue, but it is actually shown in dark green.
In summary, the manuscript omits some very important results from the literature which appear to completely invalidate the whole SIV paradigm by many hundreds of standard deviations. These results must be cited and discussed, and the conclusions amended to be less positive for the SIV model. It appears likely that the SIV model is completely incorrect, so it may be necessary to change the conclusions to reflect that.
Yours sincerely,
Referee
Comments on the Quality of English LanguageThis is fine. Just some minor instances of information that should be in brackets not being in brackets, but I am sure this will be fixed upon a more careful reading.
Author Response
We are grateful to the Reviewer for reading carefully the manuscript and for the valuable criticism and questions about our manuscript. Our answers are in blue text color within the pdf file attached as well as in the text of the paper.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsThis review is a valuable contribution to the literature on the SIV paradigm and its applications, as it summarizes the main achievements and challenges of this novel approach to gravity and cosmology. It highlights the open questions and challenges that remain to be addressed in the SIV paradigm, such as the origin and nature of the scale factor, the quantum aspects of the theory, and the compatibility with the standard model of particle physics. However, the paper could be improved by providing more details and references on the mathematical and physical aspects of the theory, by addressing some of the possible objections and difficulties that the theory faces, and by presenting more quantitative and empirical evidence that could test the validity and the viability of the theory.
(1)It does not provide a detailed derivation of the field equations and the conservation laws of the SIV paradigm, but rather refers to previous papers by the authors and others. This may make it difficult for readers who are not familiar with the SIV paradigm to follow the arguments and calculations.
(2)The abstract of the article is too long and contains too many technical details. It should be shortened and simplified to give a clear overview of the main results and contributions of the article. It is very rare for a large number of references to appear in the abstract.
(3)The introduction of the article is well-written and provides a good motivation and background for the SIV paradigm. However, it could be improved by adding some references to the recent literature on the topic, such as: Action Principle for Scale Invariance and Applications (Part I).(Refernce 19). I wonder why Reference 19 appears in Chapter 2 of the first chapter instead of Chapter 1.
(4)The Chapter 4 of the article does not provide clear conclusions or outlook for the SIV paradigm. It should be expanded and revised to highlight the main merits, shortcomings, and uncertainties of the SIV paradigm, and to suggest some possible directions for future research. Some of the questions that could be addressed, such as what are the experimental and observational tests that could verify or falsify the SIV paradigm?
(5)In the reference list, some references are not uniform in format.
Author Response
We are grateful to the Reviewer for reading carefully the manuscript and for the valuable constructive criticism and suggestions for improving the manuscript. Our answers are in blue text color below as well as in the text of the paper.
1. A suitable justifications and derivation highlights of the field equations are given on pages 7 and 8 (see equations (7-13)) with respect to scale invariant cosmology, while the equations of motions are justified on pages 6 and 7 equations (5) and (6) and further elaborated on page 15 in equations (29) and (30). It is beyond the scope of the present review to dive deep into the details since they are already give in the cited literature and at the recently dedicated paper ref [19] on the Action Principle for Scale Invariance and Applications (Part I).
2. In the abstract, we have removed the references and reduced the text from 160 to 140 words.
3. In our initial version we considered Reference 19 to be of more interest to those who would be studying the mathematical framework, now we have cited it in Chapter 1 as well.
4. We have added relevant text within Section 3.4 on page 16 and then expanded the last Chapter 4 accordingly by adding discussion on the observational tests of the z-dependence of the SIV derived MOND acceleration a0(z) see the added text in Chapter 4 on page 24.
5. In the upcoming version we plan to used BibTeX to format and order all the references.
Once again, we are grateful to the Reviewer for reading carefully the manuscript and for the valuable constructive criticism and suggestions for improving the manuscript.
Reviewer 3 Report
Comments and Suggestions for AuthorsIn this work,
the authors reviewed possible implications of the scale invariant vacuum paradigm in cosmology, with discussions on dark matter and dark energy.
In particular, the authors started providing motivations and foundations of the scalar invariant model, the mathematical frameworks and then they review the possible relations of it with MOND in galaxies and clusters. They also discuss possible deviations of this model from LambdaCDM standard cosmology.
I think that the paper can be published as a review on the subject.
I accept the paper as a review in the current form.
I also would like to suggest to the author a possible relation of the scale invariant model with the so dubbed holographic naturalness paradigm for their future studies.
Comments on the Quality of English Languagequality of English acceptable
Author Response
We are grateful to the reviewer for reading carefully the manuscript and for the suggestion about possible connection to the holographic naturalness paradigm. Although the reference suggested (https://arxiv.org/abs/2004.08372) is very interesting, at this stage of our research, we do not find this reference relevant to the discussion of the presented manuscript.
Reviewer 4 Report
Comments and Suggestions for AuthorsTitle: "The Scale Invariant Vacuum Paradigm: Main Results and Current Progress Review (Part II)"
The paper under consideration, "The Scale Invariant Vacuum Paradigm: Main Results and Current Progress Review (Part II)," presents a comprehensive overview of the Scale Invariant Vacuum (SIV) paradigm, focusing on its main results and progress to date. The abstract highlights the extension of this paradigm based on Weyl Integrable Geometry (WIG) in contrast to standard Einstein General Relativity (EGR). The following review addresses some aspects of the paper by posing relevant questions.
1. Clarification on SIV Paradigm vs. Einstein General Relativity:
Can you elaborate on how the Scale Invariant Vacuum (SIV) paradigm differs from the standard Einstein General Relativity? Specifically, what are the key distinctions in the mathematical framework and conceptual foundations between the two?
2. Density Fluctuations in the Universe:
How does the SIV paradigm provide an explanation for the growth of density fluctuations in the Universe? Could you delve into the mechanisms or processes outlined in the paper regarding this aspect?
3. Scale-Invariant Dynamics of Galaxies:
Can you provide additional information on the application of the SIV paradigm to scale-invariant dynamics of galaxies? What specific features or phenomena in galactic dynamics does the SIV theory address?
4. SIV Paradigm and Early Universe Inflation:
How does the SIV paradigm address the issue of inflation in the early Universe, as mentioned in the abstract? Could you elaborate on the implications and predictions made by the SIV theory in the context of early Universe dynamics?
5. Mathematical Framework and Weyl Integrable Geometry:
Can you explain the mathematical framework behind the SIV paradigm, particularly its connection to Weyl Integrable Geometry? How does this mathematical formalism extend or modify the understanding derived from the standard Einstein General Relativity equations?
6. SIV Paradigm and MOND Relationship:
In what way does the SIV paradigm relate to the concept of Modified Newtonian Dynamics (MOND)? Could you elucidate any peculiar cases or unique features of MOND that are explained by the SIV theory?
7. Local Dynamical Effects and Lunar Recession:
Could you provide more information on the local dynamical effects within the SIV paradigm as pertained to the lunar recession? What specific aspects of the Earth-Moon system are considered, and how are these accounted for in the SIV theory?
8. SIV Paradigm and Big-Bang Nucleosynthesis:
How does the SIV paradigm address the issue of Big-Bang Nucleosynthesis, as indicated in the abstract? Are there distinctive predictions or deviations from standard cosmological models that the SIV theory introduces in this context?
9. Differentiators of SIV from ΛCDM:
Can you explain the possible differentiators of the Scale Invariant Vacuum (SIV) paradigm from the ΛCDM model, based on insights presented in your earlier paper? What key aspects or observations distinguish SIV from the standard cosmological model?
10. Matter Required to Break Scale Invariance:
How much matter is needed, according to the SIV paradigm, to break scale invariance in the field equations of general relativity? Are there specific conditions or thresholds outlined in the paper regarding the impact of matter on scale invariance?
Furthermore, to strengthen the scholarly foundation and facilitate a more comprehensive understanding of the Scale Invariant Vacuum (SIV) paradigm, it is recommended that the authors consider incorporating discussions and references from relevant works in the field. Notably, the following reference could be integrated into the manuscript:
"Probing bounce dynamics via Higher-Order Gauss-Bonnet
modifications." Physica Scripta (2023).
In conclusion, this paper presents intriguing developments within the Scale Invariant Vacuum paradigm, and addressing these questions would enhance the understanding of its theoretical underpinnings and implications across various cosmological scales.
Author Response
We are grateful to the Reviewer for reading carefully the manuscript and for the valuable constructive criticism and suggestions for improving the manuscript. Our answers are in blue text color within the attached pdf as well as within the text of the paper.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsI am still not convinced by the arguments raised in the present work. First of all, the authors are very unclear about just how much of the observed lunar recession should be due to tides and how much due to anomalous SIV effects. The impact of tides is fairly well understood, but it seems to me like these would have to be grossly overestimated in order to leave enough room for the anomalous SIV contribution to the lunar recession. Secondly, the angular rate of acceleration of the Moon (which can be given in SI but ought to also be given in arcseconds per century squared to be consistent with literature values) still seems to be outside the range allowed by the SIV model advocated by the authors. It seems to me like even if Omega_M were reduced to almost zero, it would still not be possible to explain the observed value, which is by now extremely precisely known thanks to lunar laser ranging data, as clarified in Banik & Kroupa (2020). Thirdly, I am far from convinced by a fifty year old paper about stellar evolution supposedly showing that it is totally fine if the gravitational parameter GM of every star rises proportionally to time t since the Big Bang. Many modern studies and observational constraints on this issue were considered in Banik & Zhao (2020), so even if such a variation was allowed in 1977, that does not mean it would be allowed today.
In short, I strongly recommend that Symmetry reject this manuscript given the general attitude of the authors that there are no problems with the SIV model. This review article does not accurately capture the current knowledge regarding SIV and the observational constraints upon it. The journal may wish to consult other referees to get their opinion on this matter.
Author Response
While we respect Reviewer 1's opinion, we emphasize that there two main points raised by the reviewer:
1) “… unclear about just how much of the observed lunar recession should be due to tides and how much due to anomalous SIV effects...”
The answer to this objection has been given clearly in eqs. (36-40), (A55), (A56);
2) “… angular rate of acceleration of the Moon ...”
This point has been addressed in the appendix with eqs. (A55) and (A56) along with the discussion surrounding (A56).
3) “… I am far from convinced by a fifty year old paper about stellar evolution supposedly showing that it is totally fine if the gravitational parameter GM of every star rises proportionally to time t since the Big Bang...”
How old is a scientific paper is of no relevance to the understanding of natural phenomenon!
Reviewer 4 Report
Comments and Suggestions for AuthorsAfter carefully reviewing the revised manuscript, I find it to be thoroughly revised and addressing all previous concerns. The clarity of the writing and the robustness of the research make a compelling case for its acceptance. I recommend its acceptance without reservation.
Author Response
We are grateful to the Reviewer 4 for reading carefully the thoroughly revised manuscript and for the positive comments on the manuscript despite that the journal has rejected the manuscript. So, we use this opportunity to submit our Appeal of Rejection Decision along with the relevant communications with all four the reviewers of which three were positive and supportive while the only negative comments of reviewer 1 can been seen to have been addressed fully.
Author Response File: Author Response.pdf
