Relativistic Cosmology with an Introduction to Inflation

Round 1

Reviewer 1 Report

• The sentence, “interactions of the universe because the geometrical structure of it”, has a bad structure. Re-write it;
• The “onto physical space each point of it represents a physical location in physical space” has the same problem with before;
• When reviewing the related work, certain sentences are improper. You can find the similar sentence in the following website that can help you how to review your work. 
  https://link.springer.com/article/10.1007/s10462-017-9559-1
  https://www.mdpi.com/2227-7390/8/9/1415
  https://www.sciencedirect.com/science/article/pii/S0957417420310848
• For “The graceful exit problem was addressed independently by Linde, Steinhard and Albrecht”, insert “,” after “Steinhard”;
• The citations in “perturbations during the phase of slow roll inflation is inversely proportional to the motion of the scalar field [25–31]” are improper; citing so many papers once is not professional.
• The structure of the paper is too detailed. Shorten it.
• For “section 9 is devoted to the discussion of cosmological problems faced by the standard model”, change “section” to “Section”; Remove the similar problems in the paper;
• The mathematical symbols used in “Figure 2. The rotation of two dimensional rectangular coordinate system through angle theta” are wrong;
• The “Where” below Eq. (11) should be “where”. Remove the similar problems in your paper.
• The “Where” below Eq. (145) has the same problems with before;
• The sentence, “The set of equations in Eq. (23) is known as Galilean transformations”, has a bad structure. Re-write it;
• The figure “Figure 5. a spacetime frame as null cone structure” looks so vague. It must be redrawn and further refined;
• The “Figure 6. Structure of spacetime where one second of time along time axis equals 300000 km along the space axis” has the same problem with before;
• The “Figure 10. The geometry of 2-sphere embedded in three dimensional Euclidean space” has the same problem with before;
• The “Figure 16. History of the universe beginning with big bang and expanding with inflation” has the same problem with before;
• In general, all variables and Greek letters should be in italic format, and all constants should not be in italic format. Vectors or matrix variables should be in bold and italic format. Please double check the equations used in the manuscript.
• The mathematical symbols used in “Figure 13. A source S radiating electromagnetic enrgy” are wrong;
• The “enrgy” used in “Figure 13. A source S radiating electromagnetic enrgy” may be wrong. The authors should be double-check it.
• Except the methods used in the paper, some of the most representative computational intelligence algorithms can be used to solve the problems, like monarch butterfly optimization (MBO), earthworm optimization algorithm (EWA), elephant herding optimization (EHO), moth search (MS) algorithm, Slime mould algorithm (SMA), and Harris hawks optimization (HHO). these must be clearly pointed out in Section Conclusion.

Based on my above comments, I proposed that the paper is accepted with major revision.

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Reviewer 2 Report

This article gives a textbook-like overview of modern cosmology and inflation. All the detailed derivations are provided as educational materials. 

One overall suggestion I have is to connect the inflation models with observational efforts. Currently, there are several experiments, including BICEP/Keck, CLASS, Simons Observatory, CMB-S4, trying to detect the CMB polarization signatures of the inflation. I think the paper will be more comprehensive to link theories to current observational efforts.

There is a minor mistake I found in the manuscript in Line 225: isotropy does NOT imply homogeneity. This is also illustrated in Figure 8 of this manuscript.

Given the length of this manuscript, inevitably there are many typos. I think it will be beneficial to proofread it more carefully.

The ones I encountered are:

1. Line 75: Yong Cai1 et al.
2. Line 286: connoted in it in
3. Line 304: invariance In spatial
4. Line 337: it mans
5. Line 464: vanishinf
6. Between Equation 222 and 223: Now from from
7. Equation 227 and 228: are they supposed to be greater-than and less-than symbols?
8. Equation 230: I think this equation did not render as intended
9. Line 515: Light-an
10. Line 603: Sremains
11. Line 666: waves-waves
12. Equation 334: derivation in this equation can be perhaps written separately
13. Line 698: differentiating
14. Line 706: can described
15. Line 707: e-folds And 2nd is defined as
16. Line 708: written We have
17. Line 721: supposedlyly

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Reviewer 3 Report

This is a very good review article on relativistic cosmology, including inflation. However, I have 3 recommendations:

1. In view of the importance of the accelerated expansion of the universe, and dark energy, I suggest that the authors include a brief section on dark energy, i.e., the Lambda-cold-dark-matter-model. This is the most important unsolved problem in cosmology today.
2. The English needs to be improved, preferably by a native-speaking English person.
3. The appendices should be changed to Appendix A, B, C and D rather than P, R, S and T. Also the equations in the appendices do not need to have the prefix A in their numbering.

If the authors attend to the above three points, I would be happy to recommend the article for publication.

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Reviewer 4 Report

The authors analize an aspect of the Inflation in the contest of a relativistic cosmology. The paper is not original, in the sense that it is a review paper of the cosmological arguments. On the other hand the authors already in the abstract they say that it is a "review article". The paper is burdened by a scholastic excess of mathematical passages, but if the if the purpose is to help students get into the subject, then it can be tolerated. keeping this in mind then my judgment is positive and the paper can be published. If you consider the paper as original then my opinion is not positive and cannot be published.

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Reviewer 5 Report

The proposed review is devoted to discussion of standard cosmology with more attention to mathematical aspects. There are following points which should be clarified much better.

1. The introduction is not complete. The authors do not know many modern reviews on current cosmology. For instance, at least in the introduction they should say about dark energy epoch (which is also nearly deSitter) with corresponding review.
2.  when they study the expectation value of EMT the corresponding solutions should be described with more detail, see review Sov.Phys.JETP 51 (1980) 9-13, Zh.Eksp.Teor.Fiz. 78 (1980) 20-27
3. 3. If the authors decided to talk about R2 inflation they should then give much better introduction to inflation in modified gravity- see Phys.Rept. 509 (2011) 167-321;Phys.Rept. 692 (2017) 1 (and refs therein). At least briefly the inflation in other modified gravities as well as unification of inflation with DE should be discussed for the benefit of the readers. Major revision is requested.

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

The revised paper is resubmitted to “ Universe ”. This version is significantly better than before. All comments have been considered, so the paper can be accepted in this revised version.

Reviewer 5 Report

sufficient revision