Review Reports

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

See attached file

Comments for author File: Comments.pdf

Comments on the Quality of English Language

It seems in general fine.

Author Response

The answers are in the attached file. 

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

In this article a consideration in terms of a nonrelativistic quantum mechanical problem for the Cornell potential in the Lobachevsky space is proposed. The organization is prepared in a scientific style and several numerical results are given. In this sense this work might be worthy of being published in a scientific journal. However the contents and investigations are not so enough as an ordinary article in an established scientific journal and the current manuscript seems to be a kind of a communication. More constructive points are raised below.

1.There would be exist more recent related works of particle cosmology and astroparticle physics in terms of the issue of bound states for physical systems consisting of quarks in the literature. The important results found in this work compared with the past related similar works should be explained in more detail so that the difference of this work from the past similar articles can be much more clear.

2.For the Friedmann-Lobachevsky spacetime with a radius of curvature slowly varying in time a two-quark system is studied under the presence of the Cornell potential. From such analyses what fundamental physics in the early universe and in terms of gravitation can be found?

3.It is concluded that in the Lobachevsky space the Cornell potential has a finite depth and thus the number of bound states of the system is finite. What physical mechanism can lead to such a consequence?

4.It is strongly recommended that more astroparticle and cosmological investigations should be executed for a publication as an article in an established scientific journal.

Comments on the Quality of English Language

Minor editing of English language required

Author Response

1. There would be exist more recent related works of particle cosmology and astroparticle physics in terms of the issue of bound states for physical systems consisting of quarks in the literature. The important results found in this work compared with the past related similar works should be explained in more detail so that the difference of this work from the past similar articles can be much more clear.

 

    Ans.:   There is a huge literature on quarkonia spectroscopy based e.g. on the Cornell potential in the usual, Euclidean space, but we are not aware of relevant studies and possible new effects coming from the non-Euclidean spacetime. 

 

2. For the Friedmann-Lobachevsky spacetime with a radius of curvature slowly varying in time a two-quark system is studied under the presence of the Cornell potential. From such analyses what fundamental physics in the early universe and in terms of gravitation can be found?

 

Ans.:  The authors believe that in the early Universe, which is the Friedman-Lobachevsky Universe, the distances between quarks are comparable to the radius of curvature of space, their energy is high and there are no bound states. As can be seen from the formula for the Cornell potential in the Lobachevsky space, with a sufficiently small radius of curvature, the potential well disappears.

 

3. It is concluded that in the Lobachevsky space the Cornell potential has a finite depth and thus the number of bound states of the system is finite. What physical mechanism can lead to such a consequence?

 

 Ans.:  As it is mentioned in the article the choice of the Cornell potential is generally ambiguous. We proceeded from the fact that the first term is a fundamental solution of the Laplace-Beltrami equation in three-dimensional Lobachevsky space and sought to preserve the symmetry inherent in the flat limit of this potential. In the formula, the first term corresponds to the Coulomb attraction, and the second to the linearly increasing potential in flat space.

 

4. It is strongly recommended that more astroparticle and cosmological investigations should be executed for a publication as an article in an established scientific journal.

Ans.: The use of Friedman-Lobachevsky spacetime already implies the use of a cosmological model. 

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

See attached file.

Comments for author File: Comments.pdf

Comments on the Quality of English Language

It seems fine.

Author Response

The answers are in the attached file. 

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The authors' answers and revision are appreciated. The points in the review report have been considered. It seems the revised manuscript could be suitable for publication.

Comments on the Quality of English Language

Minor editing of English language required

Author Response

Thank you. We are doing our best to improve the language.