A Scale Invariant Fully Conformal Cosmological Model and Its Support by Astrophysical Data^†

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

1. comment

"The coefficient of determination R² = 0.9821 of the fit in Fig. 1 documents a good agreement with the experimental data and confirms the realistic nature of the mathematical formula of the generalized Hubble-Lemaître law (20)."

Please clarify the actual meaning of the use of the word "good". There are statistical methods to quantify the acceptability of a fit.

I ask for a similar one after Fig2, here: "The fit has a coefficient of determination R² ≈ 0.888 in the region Cmax/Cmin ≥ 10."

 

2. comment

Please summarize the above in a concise paragraph at the end of Chapter 3 (as a translation of the derivations), thus facilitating the reader's understanding and significantly improving the proper reception of the information provided later.

 

 3. comment

"RELATIVITY OF OBSERVER TIME AND THE APPARENT AGE OF THE UNIVERSE":

Is the passage in brackets below, written in italic, a quotation? If so, please show clearly that you mean a quotation.

" (Here, however, two fundamental differences should be emphasized: in a scale invariant and fully conformal universe, expansion has only a relative observational character, similar to mass in special relativity, and the time-invariant global energy-momentum tensor does not require the continuous creation of new matter, unlike the familiar steady-state model) "

 

4. comment

"SPATIAL DISTRIBUTION OF γ-RAY BURSTS" chapter:

Are there earlier GRB data than those used in the article? Could the Swift, Fermi data be used? Why did you work with BATSE data from the 2000s?

 

5. comment

 

Please investigate to what extent the spatial distribution of GRBs and quasars can be considered homogeneous. Does this influence the results of the paper?Over the last decade, several studies have shown that both GRBs and quasars are not uniformly distributed in the Universe. In fact, their redshifts show peaks for given redshift values.

Author Response

 

1. REVIEWER

comments 1

"The coefficient of determination R² = 0.9821 of the fit in Fig. 1 documents a good agreement with the experimental data and confirms the realistic nature of the mathematical formula of the generalized Hubble-Lemaître law (20)."

Please clarify the actual meaning of the use of the word "good". There are statistical methods to quantify the acceptability of a fit.

I ask for a similar one after Fig2, here: "The fit has a coefficient of determination R² ≈ 0.888 in the region Cmax/Cmin ≥ 10."

response 1

Thank you for pointing out the unclear wording and I added the requested clarification:

R² represents a measure of the quality of the regression model - 100∙R² indicates what percentage of the variance of the explained variable is explained by the model.

THE REQUESTED CHANGES HAVE BEEN MADE IN THE MANUSCRIPT:

• The coefficient of determination R² = 0.9821 in 1 documents approximately 98% fit of the model regression function to the observational data and confirms the realistic nature of the mathematical formula of the generalized Hubble–Lemaître law .
• The coefficient of determination R² ≈ 0.888 demonstrates approximately 90% fit of the regression model function to the observational data in the region C_max/C_min ≥ 10.
• The calculated coefficient of determination R² ≈ 0.9511 demonstrates approximately 95% fit of the regression model function to the observational data for the first six points.

 

comments 2

Please summarize the above in a concise paragraph at the end of Chapter 3 (as a translation of the derivations), thus facilitating the reader's understanding and significantly improving the proper reception of the information provided later.

response 2

I understood the reviewer's suggestion as an overall summary of the degree of model fit to the observational data and found it very useful for further understanding of the subsequent information.

I placed that summary at the end of Chapter 6, which contains the last confrontation with observational data (quasars).

 

comments 3

"RELATIVITY OF OBSERVER TIME AND THE APPARENT AGE OF THE UNIVERSE":

Is the passage in brackets below, written in italic, a quotation? If so, please show clearly that you mean a quotation.

" (Here, however, two fundamental differences should be emphasized: in a scale invariant and fully conformal universe, expansion has only a relative observational character, similar to mass in special relativity, and the time-invariant global energy-momentum tensor does not require the continuous creation of new matter, unlike the familiar steady-state model) "

response 3

Thank you for bringing this to my attention. This is not a quote, but a highlighting of the above statement. To avoid confusion, I removed those brackets and changed the sentence to standard text.

 

comments 4

"SPATIAL DISTRIBUTION OF γ-RAY BURSTS" chapter:

Are there earlier GRB data than those used in the article? Could the Swift, Fermi data be used? Why did you work with BATSE data from the 2000s?

response 4

The derived function N(C_max/C_min) is compatible with the BATSE source data format. Confrontation with data from Swift, Fermi would certainly be very interesting, but it was beyond the author's ability to do the data conversion.

 

comments 5

Please investigate to what extent the spatial distribution of GRBs and quasars can be considered homogeneous. Does this influence the results of the paper?Over the last decade, several studies have shown that both GRBs and quasars are not uniformly distributed in the Universe. In fact, their redshifts show peaks for given redshift values.

response 5

The real homogeneous space-time distribution of astrophysical objects is the underlying assumption of the model due to the initial acceptance of the "perfect cosmological principle". The observed non-constant distributions are due to the effect of the conformal metric on the COP proper coordinates.

 

 

Submission Date

23 November 2024

Date of this review

14 Dec 2024 11:37:21

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

The authors has discussed about the new interpretation of the simple solution of Einstein's equations within a fully conformal metric in view of  a time-independent energy-momentum tensor. The scaling factor here acts identically on all four space-time coordinates and the speed of light is independent of the conformal time. The conformal metric is interpreted as a universal geometric background. Further, it is invariant and acts universally on all objects, including gauges and clocks, regardless of their dimensions and internal interactions. This type of interpretation leads to the associated expansion is only relative and all observers at different times are completely equal. The implications of the fully conformal metric are confronted with astrophysical data such as cosmological redshift and the observable spatial distribution of quasars and γ-ray bursts. On a cosmological scale, the fully conformal metric naturally determines energy density and spatial flatness, and solves the horizon problem and Olbers' paradox in infinite spacetime.

The author’s approach is unique and definitely, it will attract the larger audience for the further research. It seems all the derivation involves in this article are correct. Thus, it is recommended for the possible publication in your journal.

Author Response

2. REVIEWER

comments 1

The authors has discussed about the new interpretation of the simple solution of Einstein's equations within a fully conformal metric in view of  a time-independent energy-momentum tensor. The scaling factor here acts identically on all four space-time coordinates and the speed of light is independent of the conformal time. The conformal metric is interpreted as a universal geometric background. Further, it is invariant and acts universally on all objects, including gauges and clocks, regardless of their dimensions and internal interactions. This type of interpretation leads to the associated expansion is only relative and all observers at different times are completely equal. The implications of the fully conformal metric are confronted with astrophysical data such as cosmological redshift and the observable spatial distribution of quasars and γ-ray bursts. On a cosmological scale, the fully conformal metric naturally determines energy density and spatial flatness, and solves the horizon problem and Olbers' paradox in infinite spacetime.

      The author’s approach is unique and definitely, it will attract the larger audience for the further research. It seems all the derivation involves in this article are correct. Thus, it is recommended for the possible publication in your journal.

response 1

I thank the reviewer for the positive review and I hope that the article will be accepted for publication in UNIVERSE after editing. At the same time, I am finishing a follow-up paper that focuses on a modification of the Schwartschild solution within the conformal model, the equation of state and a new concept of the CMB.

 

 

 

Datum podání

23. listopadu 2024

Datum této recenze

19. prosince 2024 14:39:13

Author Response File: Author Response.docx

Reviewer 3 Report

Comments and Suggestions for Authors

Report on Ms. universe-3360028

The author presents a detailed study of a conformal cosmology, including applications to astronomical data.  In principle, the work is valuable although with a few weak points.    However, a severe objection against publication in Universe or any other journal is that the author has published in 2023 a paper of the same subject and with almost the same content on SSRN. Since that paper is neither cited nor mentioned otherwise, the present submission is an unacceptable resubmission of already published work, if not a suspicious case of self-plagiarism. The paper must be rejected. Comments on the Quality of English Language

 No comment

Author Response

3. REVIEWER

comments 1

The author presents a detailed study of a conformal cosmology, including applications to astronomical data.  In principle, the work is valuable although with a few weak points.    However, a severe objection against publication in Universe or any other journal is that the author has published in 2023 a paper of the same subject and with almost the same content on SSRN. Since that paper is neither cited nor mentioned otherwise, the present submission is an unacceptable resubmission of already published work, if not a suspicious case of self-plagiarism. The paper must be rejected.

response 1

The work is a new modified and extended version of PREPRINT on the preprint server SSRN: Dvorsky, Richard, A Simple Fully Conformal Solution of Einstein's Gravitational Equations and the Agreement of its Implications with Astrophysical Data (March 1, 2023). Available at SSRN: https://ssrn.com/abstract=4373727 or http://dx.doi.org/10.2139/ssrn.4373727

This reference is inserted as a note in the conclusion following a reviewer's comment.

 

Journal Universe, published by MDPI, allows preprints to be pre-published on the SSRN preprint server in accordance with its policies. Preprint servers operate independently of journals and publishing a preprint does not affect the peer review process. Therefore, I do not believe that the aforementioned preprint is an obstacle to publication in the peer-reviewed journal Universe. The bizarre formalistic concept of "self-plagiarism" should not be used as an excuse to suppress the possibility of disseminating a new idea to the wider scientific community.

 

 

 

Submission Date

23 November 2024

Date of this review

22 Dec 2024 16:36:05

 

 

 

Author Response File: Author Response.docx

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

Report on Ms. Universe-3360028

The author presents a conformal cosmology incorporating the cosmological principles,  leading to a scale invariant formulation . The model is used to study various observables from the Hubble-Lemaitre  law to the distribution of astrophysical sources. The whole approach is an interesting alternative to the existing formulations. The paper is an updated version of a previous work published online as a preprint on SSRN. The work is shedding  new light on  cosmological modeling. The paper will be of interest for the astrophysics community. The slightly revised paper is recommended for publication.