Vacuum Polarization Instead of “Dark Matter” in a Galaxy
Round 1
Reviewer 1 Report (New Reviewer)
In this paper, authors examined two types of vacuum polarization within a galaxy in the eikonal approximation. The first polarization follows the equation of state of radiation. Assuming that a compact object , e.g., a black hole, resides at the galaxy center, The authors showed that conformally-unimodular metric provides a nonsingular vacuum solution for this dark radiation. Then this dark radiation is interpreted as a dark galactic halo which changes the rotation velocity curve of the galaxy. The second type of polarization, in its static state, is used to for renormalization of the gravitational constant while in its nonstationary state, is explained as a dark matter halo.
I have some questions for the authors before I can recommend the paper for publications:
1) Although, as the authors claimed, there is an increase in the rotation velocity of a test particle as a function of the distance from the galactic center, Fig. 5 does not provide a good fit between the observation and the model. Is it possible to find a good fit, in agreement with data for rotation curved of Milky way or any other galaxy?
2) As we know, dark matter should be cold (non-relativistic) enough to avoid erasing small-scale structures via free-streaming. How does the first polarization, which is similar to radiation, become non-relativistic in this model?
3) How is dark matter relic abundance today is explained in this model? As a measured value, how does this number constrain vacuum polarization?
4) I do not understand the footnote at the bottom of page 16. How this model explain dark matter content in galaxies without compact objects at their centers, such as ultra diffuse galaxies?
5) How can this model be tested, be ruled out or be confirmed by experiment?
Author Response
reply in pdf file
Author Response File: 
Author Response.pdf
Reviewer 2 Report (New Reviewer)
The authors have proposed and considered vacuum polarization to be an alternative to dark matter in galactic media. In particular the authors have studied two types of vacuum polarization and have extensively carried out field calculations in support of their theory. The extensive mathematics used in this work is credible and accurate and the resulting physics is scientifically sound. Other than a few minor English language and grammar corrections here and their, I have not found any major issue in this work. The manuscript is prepared professionally and the text is easy to follow. Overall I recommend publication after minor editing modifications and revision.
Author Response
Dear Reviewer, thank you very much for your notes. In the present
version we are trying to improve English language and make some
grammar corrections.
Reviewer 3 Report (New Reviewer)
This is a useful paper developing new scheme to introduce quantum features in gravity. My suggestion is to clarify the units. Once we are dealing with quantum effects in classical theory it is worth to start with units in which the Planck's constant is explicit. This could help to clarify at which cosmological scale quantum effects are important and to better understand to which epoch the author's approach can be applicable.
Author Response
reply in pdf file
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report (New Reviewer)
I believe the manuscript has been sufficiently improved to warrant publication in Universe.
Reviewer 3 Report (New Reviewer)
I am satisfied by additions made by the authors, and I have no more objections
for publishing the paper
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
This is a very interesting paper which describes how the rotation curves of galaxies could be ascribed to a completely different cause than "dark matter", and be due to properties of the vacuum.
I should point out that I work as on observations to measure the amount of dark matter in galaxies, and have no expertise in the theoretical side of the problem addressed in the paper.
If the editors would like a review from a theoretician, then that might be appropriate next step. I leave that to the editors of the journal.
What I thought I could do is provide some feedback on the text of the paper to help with the presentation, which I attach as an annotated PDF. I hope they are useful (note I am a native English speaker).
While I cannot comment with any authority on the theory, I can comment on comparisons to observations.
Figure 5 shows a comparison of the theory with data.
I think it would be *very important* to show the error bars on the observational data points.
They are *very large* in the outer regions where the one aspect of the model is aiming to fit the data.
What exactly the data are showing at radii as large as 1 Mpc from the Milky Way is very unclear at least in my mind as an observer.
For example, the Andromeda galaxy is only 0.7 Mpc away, so at these distances, we are talking about two galaxies, and not 1, within the radii probed.
Additionally, at small radii, the data points are affected by the supermassive black hole at the Milky Way center -- it is unclear to me whether the model is aiming to fit these data points with a vacuum polarisation effect, ignoring the black hole -- or whether it is able to obviate the black hole's existence as such.
Another comment is about the authors' proposal that the nuclear region could represent a rapid change ("swift increase" is the term used in the abstract) in the potential with a time scale of order 32,000 years and producing a "dark halo" of scale size ~10 kpc -- which would then persist to the present day (?).
I am not a theoretician, and it may be that I have this idea completely muddled -- but that's a good feedback to give as undoubtedly other readers could also be confused by this. I think the exact idea needs to be spelled out more careful to a reader like myself so that we grasp the principle.
The inability of the theory to provide a scale for the Vrot axis in Fig 6 will be regarded as a serious weakness by many readers. I don't understand the reason for this (I gather it's not an oversight be the authors) -- I think an explanation of this would be very helpful.
I am not sure the outline of the paper at the end of Section 1 is correctly aligned with the present structure -- there seem to be more sections in the real paper than mentioned in the summary, and there might be an "off by 1" problem in the sections as summarised. Could the authors double check this?
Comments for author File: Comments.pdf
Author Response
The notes are in pdf file. All the best.
Author Response File: Author Response.pdf
Reviewer 2 Report
Dear Editors, Dear Authors,
I cannot recommend this paper for publication in the “Universe”.
My comments are as follows.
11. Authors either consider an essential modification of general relativity, or made a mistake. E.g., Equation (7) is not the standard Friedman equation. One has to replace the multiplier in the right hand side with $\rho +3p$ (the correct sign here is plus). Otherwise this is not the Friedman equations.
22. Authors introduce a cutoff in the momentum space and observe that the equation of state for vacuum becomes $p=\rho /3$. Everyone who started the studying of quantum field theory knows this phenomenon (for more than 70 years) and knows that this is not true. Such a cutoff violates Lorentz invariance of the vacuum state and this can be observed in laboratory experiments. But so far any violation at laboratory scales was not detected. The standard regularizations lead to the vacuum energy density that reproduce the cosmological constant ($\rho = -p$). Moreover, such an equation of state was verified in QCD. This authors approach leads to numerous mistaken conclusions.
33. Authors based on their cutoff find too strong effects of the polarization of vacuum. It seems they tightly follow the existing fashion. Some phenomenological theories predict corrections to general relativity which are strong enough to produce strong effects at cosmological scales. There is no any rigorous paper which shows that quantum corrections may produce such an enormous effects. Unfortunately, there are only waving hand arguments in virtue of possible existence of such strong modifications. Most of them are considered as pure phenomenological theories inspired by inconsistencies in observational data (e.g. the presence of dark matter). Any rigorous consideration shows that quantum vacuum polarization effects are negligible at galaxy scales. Authors should know that the gravitational potential even in the center of a galaxy is much smaller than that on the surface of our Earth. Therefore, any noticeable effect should be detected here. The standard consideration shows that such effects are important near the horizon of black holes (e.g., they leads to well-studied phenomenon like Hawking radiation, etc). But this is not sufficient to say seriously about dark matter. Though corrections to the vacuum equation of state admit this. But they are too small. I think if authors will perform first the renormalization of basic constants (e.g. the gravitational constant) even in their approach, then they find actual negligible value of polarization effects on galaxy scales.
Best regards
Reviewer
Author Response
The notes are in pdf file. All the best.
Author Response File: Author Response.pdf
Reviewer 3 Report
The computations seem correct as well as the conclusions. The model proposed seems to be an interesting extension of the more familiar approaches in this context. Because of this, I am inclined to propose the publication in its current form. However, I would like the authors to pay attention to
1) Although it could be a matter of style, there are expressions that are not suitable, in my opinion, for a scientific text. Using a hole in a socket as an analogy for removing a point is too informal. So it is calling something "mystical".
2) For the sake of clarity, for the potential readers, the authors should have included the equations of motion yielding the equations (3) and (4). Citing Ref.[6] is not enough. In particular, I would like the authors to make a comment, from first principles, in how traditional black holes and eikonals yield such radical different physical scenarios.
Author Response
The notes are in pdf file. All the best.
Author Response File: Author Response.pdf
Reviewer 4 Report
The first part of this work, that aims at describing large scale structure and local dark matter distributions, is extremely confusing. It is not clear to readers why one passes from "unimodular metric" to spatially flat FRW and vice versa.
The paper argues, indeed, to describe even cosmic acceleration using a strategy that, again, is not well-reported in the text. In addition to that, the structure of the manuscript in which dark matter is described implies considerations that are clearly wrong.
First the approximation is only valid for quantum fields, here not considered.
Second dark matter EoS is identically zero by construction, if one requires no interaction for dark matter.
Third the corresponding 1/3 would imply a coupling with electromagnetism that would reveil dark matter, but as far as we know dark matter is dark, and does not bright at all
Moreover, even the rest of the manuscript is extremely hard to be understood. It's not clear the metric structure behind the authors' choice and what they intend to demonstrate.
Honestly speaking this work has serious drawbacks that are related to physics and for these reasons it is not reasonable enough to be considered for publication.
Author Response
The notes are in pdf file. All the best.
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
Dear Editors
Authors did not improve their manuscript.
I did two essential comments
1. Eq 7 is wrong. It contradicts the history of our universe. According to 7 the radiation dominated epoch was absent.
2. Cutoff at planck scales eq.11 gives too enormous density of vacuum energy. Since cutoff is introduced in such a way, that it violates the Lorentz invariance of the vacuum, it can't be remormalized in the standard way and this produces too strong effects already in the Newton' s theory e.g. such must be observed in laboratory experiments and on the planetary scales.
Only due to wrong eq. 7 such contribution cancels in author's theory.
I do not think it is worth considering the contribution of vacuum energy to rotation curves before analyzing analogous effects at earth. Author's estimates either wrong, or make too strong problem for satellites. Why they follow the Newton theory on Earth? Why any corrections are small?
Best regards
Reviewer
Reviewer 4 Report
The paper is based on wrong considerations as already I stated once. There's no change that can modify my idea since the idea is still the same that is clearly unphysical. The reasons are reported in my previous report.
