Does the Cosmological Expansion Change Local Dynamics?
Round 1
Reviewer 1 Report
The author checks the possibility to have first order perturbations of the cosmic space-time smooth background due to the local presence of masses and finds no such situation in the case of the non-standard theories he considers, but in the end remarks that, should the linear perturbations exist, they would be important. The paper is thus, though correct, rather inconclusive.
Formal remarks.
Of course the reader can look to the references for detailed definitions, but a paper should be as self-contained as possible. For this reason it would be useful to have parameters and conventions more explicitly exposed in the introduction.
There are a number of misprints. A careful re-reading of the text is in order. A few examples of the quoted misprints (there are more) are:
Page 1, column 1, second line from bottom: “halo”, not “hallo”
Page 2, column 2, second line after eq. 12: “Friedman” (not “Friedmann”).
Page 7, column 1, fifth line before section “Spinor Field”: “he” should be “the”
Page 9, column 2, second line after Eq. 117: “he” should be “the”
With these amendments I think the paper may be published.
Author Response
We thank the reviewer for his constructive remarks. The manuscript has been revised and typos have been corrected. The paper is conclusive in the sense that fields of the sort reviewed in the paper cannot amend General Relativity to yield flat rotation curves as a consequence of the expansion of the Universe
Reviewer 2 Report
The paper Does the Cosmological Expansion Change Local Dynamics? by M. Schiffer addresses very important questions: is gravity affected by cosmological expansion in the weak field regime, to the point to of requiring either the formulation of a MOND or the assumption of dark matter? This very possibility requires the discussion of scalar, spinors or non-gauge vector fields. The author then develops a perturbation analysis of the field equations. I did not thoroughly follow the calculation, but noted no gross inconsistencies. The first part of the paper provides a confirmation of an established result. The second part discusses the role of a spinor field in affecting the gravitational potential with a linear term correction in H. The general conclusion is reasonable.
It would be beneficial to expand the introduction and the conclusion part with a few more sentences about astrophysical implications. For example, the connection between the Tully-Fischer law and the linear term in H could be further explained. A graph showing the relevance of the linear term with respect to the Newtonian one in the velocity profile would be also useful.
Author Response
We wish to thank the reviewer for his constructive remarks. The paper has been slightly reviewed. In the conclusions we removed the discussion of the linear term, as we figured out that It would be problematic at distances much larger than $5kpc$. In the concluding remarks, at the end of the paper we added a speculation of what kind of expansion could provide the flat rotation curves.
Reviewer 3 Report
The paper is interesting and well-written. I recommend the paper for publication after some changes. In the whole paper the author has to put comma and dot after equations as needed. There is no a Discussion section. The author has to write the Discussion section and, also, to specify the existence of this section at the end of the Introduction. In this light, I also propose that the section Dark Matter or Modified Gravity to become Introduction.
Author Response
We wish to thank to referee for his constructive remarks.
We transformed the chapter "Dark Matter or Modified Gravity" as the introduction of the paper, and stated the existence of a concluding remarks section where our results are discussed and speculated the difference difference powers of the Hubble constant makes. The final discussion is now named "concluding remarks". Dots and commas have been reviewed along all the equations in the manuscript.
Reviewer 4 Report
Dear Editors,
In my view, the manuscript does not contain enough scientific material for the publication in this journal. I appreciate the author’s motivation at the basic level that the contribution from the Hubble expansion may explain the peculiar feature of the dynamics in galaxies. It also seems there are no serious mistakes in the technical computations, and I agree with the author’s conclusion that the contribution from the Hubble expansion is negligibly small for the two models (Brans-Dicke theory and spinor field). However, I do not understand why the author chose these two models for the present purpose. As for the BD theory, the experiments already constrain that BD theory must be very close to GR, which means that the scalar force is much more suppressed compared to the gravitational force. Thus, it is unrealistic that the scalar contribution dominates over gravity at the galactic scale, and there is no physical motivation to study the current problem within the framework of the BD theory. The same argument applies to the case of the spinor field.
In the very last paragraph, the author states that presence of a linear term $Hr$ in the gravitational potential, which may be realized in some yet-undiscovered theories, can yield rotation curves which look almost flat and suggests that such a term may provides a new explanation alternative to dark matter. I do not find it reasonable; the linear term dominates at the galactic scale (about 5 kpc) and thus the rotation curves must exhibit increasing feature proportional to $sqrt{r}$ with the universal proportionality constant given by the Hubble constant for all the galaxies, which is not observed in reality.
Sincerely yours,
Author Response
We thank the reviewer for his constructive remarks. The purpose of the paper is to verify whether additional fields in conjunction with Einstein's theory could yield correction to Galactic Dynamics owing to the expansion of the Universe. Solar system experiments constraint on the Brans Dicke leaves some margin for modifications at much larger scales. Nevertheless, if not Brans Dicke , theories involving additional fields would produce similar results. The discussion of the conjecture of linear terms in the Newtonian Potential and its consequences have been reviewed.
Round 2
Reviewer 4 Report
The author's response to the first report as well as the revised manuscript do not address at all the issues raised in the first report. Because of the same reasons as in my first report, I do not recommend the revised manuscript for the publication in the journal Symmetry.
