Primordial Black Holes from Spatially Varying Cosmological Constant Induced by Field Fluctuations in Extra Dimensions
Round 1
Reviewer 1 Report
Comments and Suggestions for Authors
Please see the attached pdf file: Report--universe-2819589
Comments for author File: 
Comments.pdf
Comments on the Quality of English Language
Minor editing of English language required
Author Response
We answered to the referee report
Author Response File: Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for Authors
The authors suggest a very interesting mechanism of possible PBH formation, as reflected in the title, using some results from their previously published papers. In my opinion, such a paper certainly deserves publication. There are, however, some remarks to be addressed before that.
Main point: if a PBH formation mechanism is suggested, it would be natural to expect at least some hint or speculation on a possible mass spectrum of such PBHs and hence their relevance to the present cosmological situation. The only such hint I found as given on page 6 is "Consider the case of PBH formation as massive as 10^2-10^3 Solar mass" - this looks quite insufficient.
A technical point: the metric (3) contains $e^{2\gamma(u)}$ before the 4D de Sitter line element. How does this factor affect the 4Dob servable quantities, in particular, what justifies using this deSitter element, or (6), as our 4D metric?
It is repeatedly written that "stationary distributions of fields form a set of measure continuum" - well, it sounds nice, but what does it really mean: one free parameter? a number of these? or an arbitrary function?
In general, unfortunately, the paper is written rather carelessly: in addition to numerous language mistakes, I noticed such errors as $d\Omega_n$ instead of $d\Omega_{n-1}$ in Eq.(3) and a lost minus on line 100 (expression for \Lambda on page 3, compare with Eq.(5)). Then, how to be sure that all other equations are correct? There are logically strange statements like "the formation of gravitationally bound objects can be formed" (end of Sec. 4). Corrections are necessary.
I hope that these remarks will be taken into account in a revised version of the paper.
Comments on the Quality of English Language
Mistakes are quite numerous, including misused articles, mixed singular and plural (like "Formulae above gives" on line 200), wrongly used words (e.g. "remind"), etc.
Author Response
We answer the referee's remarks
Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for Authors
Referee report on the manuscript
"Primordial Black Holes from Spatially Varying Cosmological Constant Induced by Field Fluctuations in Extra Dimensions" by Arkady A. Popov, Sergey G. Rubin, and Alexander S. Sakharov.
In the manuscript submitted to Universe the authors suggested a new mechanism of primordial black hole formation. In particular, they taken into account the quantum fluctuation of fields and metric fluctuations in the extra-dimensional Universe during inflation. Such extra fluctuations have specific time behavior leading to formation of black holes. I think this paper is well-written and is interested for wide auditorium. Therefore, I recommend the manuscript for publication in Universe.
The authors should make minor cosmetic corrections:
1. In Line 49: There is a LaTeX-typo related with References: [55? –59]
2. In Line 41: I would recommend to put Reference on the generalized Einstein equations.
3. In the end of Introduction Line I would recommend to breifly discuss the structure of the manuscript:
The paper is organized as follows. In Sec. .....
4. After Eq.(1) I would explained in detail the notation occurring in the effective action. In particular, how the manifold is constructed, what are the Minkowski (?) and extra-dimensional indices, warping functions gamma(u) and r(u), Hubble parameter H. Some comment about quadratic dependence of the scalar potential would be useful.
5. The sentence before Eq.(4) can be slightly modified as
After integration over the extra-dimensional coordinates the action (1)
reduces to the effective action [60] ....
Author Response
We answered the Referee's remarks
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Comments and Suggestions for Authors
After making the necessary amendments, the manuscript is well within the scope of the special issue, The Friedmann Cosmology: A Century Later. Therefore, I recommend publication of the manuscript in its present form.
