Reconstructing Modified and Alternative Theories of Gravity

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Referee Opinion on the paper: Reconstructing modified and alternative theories of gravity Dalia Saha, Manas Chakrabortty and Abhik Kumar Sanyal  Universe 2770060

 

               The paper Reconstructing modified and alternative theories of gravity Dalia Saha, Manas Chakrabortty and Abhik Kumar Sanyal is connected with modified and alternative theories of gravity. The problem and present paper is interesting, however paper need improvement in some point.   1.  Already in the first sentence of the introduction, the authors write “Luminosity versus red-shift data curve associated with SN1a standard candles requires a modification of FLRW universe at the late stage of cosmic evolution.” This is not true because the FLRW Universe is a homogeneous and isotropic universe and currently such a universe is favored rather than rejected by observations (assuming the presence of Dark Energy does not force such a change because, for example, the LCDM model is still the FLRW Universe). 2.  Moreover, the FLRW model, due to the need to take into account density fluctuations, has a problem in the early phase of the evolution of the Universe rather than in the late one. 3.  In the beginning of second paragraph authors wrote: “After more than two decades of intense research, most of the scientists now believe that neither a cosmological constant, nor dark energy is responsible for solving the cosmic puzzle” . Here we conduct scientific discourse. I believe in God, but here we are talking about scientific results, so this is not the place to describe what the authors believe about the structure of the universe. Moreover, it is not true that most scientists reject the idea of ​​the existence of the cosmological constant and dark matter (regardless of the problems with explaining the value of the cosmological constant, if it is responsible for the expansion of the universe). 4.  In the case of generalized theories of gravity, an important fact is that in general these theories do not assume a relationship between connection and metric. As a consequence, the equivalents of Einstein's equations are fourth-order, not second-order equations (which leads to a number of consequences, not only the lack of the superposition principle). This issue is very important and must be discussed. 5.  This is because the authors (at the beginning of chapter 3) assume that they are considering the Robertson Walker metric. Meanwhile, the metric there is the solution we get in the case of the standard FLRW Universe (i.e. in the case of standard Einstein equations). There is no a priori reason for this metric to hold in a model universe with modified or alternative theories of gravity. 6.  As the authors wrote in the introduction, they assume that we currently live in a Universe dominated by such a modified or alternative theory of gravity, so the argument that in the radiation era the Universe was well described by the FLRW model is completely insufficient. 7.  The literature is quite sparse and does not refer to the broader context of research on generalized and alternative theories of gravity. As a result, there are no references to a number of important issues, such as Palatini formalism. The manuscript does not include a number of important works (for example, a series of works by Professor Andrzej Borowiec and citations to them)                  In my opinion, all these points must be corrected, improved and clarified before the paper can be accepted to any journal     It may be regretted that the authors did not decide to rewrite their formulas for the Hubble function in order to try to test their predictions and results using available observational data, but this would go beyond the changes of "major corrections" and I hope that the authors will make such an attempt in their next works.   Since English is not my native language, it is difficult for me to decide about the quality of English, however, I find English good enough to be understandable by the reader.

 

Author Response

Reply to report of referee-1:

First of all, we would like to thank the learned referee for thoroughly going through the manuscript thoroughly and stating it to be interesting. Underneath, we reply to all the points raised by the learned referee point by point.

1. Based on cosmological principle (homogeneity and isotropy), Friedman in 1922 and Lamaitre in 1927 independently showed that a universe filled with perfect barotropic fluid undergoes decelerated expansion ( in radiation era and  in matter dominated era). Later Robertson (1935, 1936) and Walker (1936) independently demonstrated that the metric used by Friedmann and Lamaitre provides the most general Riemannian geometry compatible with homogeneity and isotropy. After Hubble’s discovery in 1930, and as Rutherford’s proof (1931) that the static universe with a positive cosmological constant (Λ) is unstable, Einstein withdrew Λ and agreed that the universe is expanding. Since then it is dubbed as the standard model of cosmology or the FLRW model or the FLRW universe.  However, for the reason stated above the metric sometimes is called as FLRW metric. Note that the metric and the model are different. In the background of homogeneous and isotropic Robertson-Walker (RW) metric if the energy momentum tensor is modified by considering any other type of fluid (even a cosmological constant) it is not the standard FLRW model. For example, Einstein’s static universe model, de-Sitter model, the ΛCDM model etc. all are different models in the background of isotropic and homogeneous RW metric. These not to be confused with the standard FLRW model. This is a common mistake nowadays found in most of the research papers. We therefore are not making any revision in this regard. We refer to any standard authentic text book, particularly ‘Gravitation’ by ‘Misner, Throne and Wheeler’.
2. The structure formation problem is associated with the density fluctuation in the early universe, which is currently observed in the temperature anisotropy of the CMB. This is accounted for, considering perturbation in the RW metric. The real problem appears in the very early universe to account for the flatness, the horizon and the seeds of structures. This is overcome by invoking inflationary scenario, which may be driven by a scalar (Higgs) field or higher-order curvature invariant terms or else. As mentioned, in the late stage one needs to consider exotic matter with sufficiently negative pressure apart from the perfect fluid. These requirements in the very early as well as at the late-stage, are clearly deviation from the FLRW model. We don’t modify our manuscript with respect to this comment too.
3. It appears that the referee is not happy with the word “belief”. We agree, since science unlike religion does not run on belief. So we have rewritten the 2^nd paragraph of the introduction (in italics).

However, we have never stated that scientists reject the idea of the existence of the cosmological constant. Cosmological constant (Λ) is the sum of zero-point energy of all the fields (quantum) existed in the past, and there is no question on its existence in the early universe. We just stated that the huge Λ cannot be responsible to solve the puzzle. There is no viable theory that explains why Λ is so small today.

Next, we think there is a typo in the report: ‘dark matter’ should be ‘dark energy’ instead. The problem with cosmological constant and null results in search of the dark energy, motivated most of the cosmologists to search for alternatives, by modifying the left hand side of the Einstein’s equation (without considering any scalar field in the energy-momentum tensor), which is dubbed as modified theory of gravity. Also there are attempts to define gravity in terms of the torsion or non-metricity scalars. We think the revised 2^nd paragraph would not be debatable.

4. In the case of modified modified theory F(R) of gravity, the field equations are fourth order, and hence might be plagued with Ostrogradiski instability apart from the violation of superposition principle. The main virtue of telleparallel theory of gravity is that the field equations are second order as in the case of Lanczos-Lovelock gravity. However, there is a recent hint that F(Q) gravity theory with non-linear terms might also suffer from the pathology of Ostrogradski’s instability. This we have mentioned in the concluding remarks with appropriate citation.
5. We find it extremely difficult to understand the language. However, it appears the referee is trying to state that the modified or alternative theories cannot have Friedmann-like solutions. In this connection, we remind for example, that TEGR and STEGR are two telleparallel theories equivalent to GTR. As a result, Friedmann solutions automatically follows. We also remind that in modified gravity had been proposed which includes terms like or else, so that  dominates in the middle and Friedmann-like solutions result. Likewise, any higher-order or modified telleparallel theory can admit Friedmann-like solution in the middle.
6. This we have already explained. It is not only sufficient, but modified and alternative theories should be treated as viable only if these theories admit Friedmann-like solutions in the radiation and early matter dominated eras.
7. Currently, we have no concern with Palatini formalism. In future work we shall aim at it. Thanks a lot for bringing our notice to Borowiec’s work. We have gone through a few papers of Borowiec, and found that none is related to our present work. In future, we shall definitely cite these when required.

Referee finally states ‘all these points must be corrected, improved and clarified before the paper can be accepted to any journal’. We are honoured to learn that the learned referee has the authenticity to all the journals in. However, we are currently concerned with a particular journal, the universe (MDPI). It’s true that we have not tried to compare our results with observational data in connection with the Hubble’s parameter. The reason being, we have not solved the field equations for the late-stage of cosmic evolution in F(T)/F(Q) gravity, which is done by several authors earlier. Rather we have shown that the inflationary parameters fall within observational constraints. Nonetheless, for F(R) gravity we cited a paper (currently ref. 18) where theoretical predictions were matched with the observational data.

In a nutshell, we think that we have clarified all the issues raised by the referee, point by point and improved some of these along the line suggested by the referee.

 

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The paper introduces the three standard and less-standard ways in which gravity is nowadays built (according to whether the gravitational information is encoded within R, T or Q), and proceeds to discuss the respective enlargements (in terms of f(R), f(T) and f(Q) as they are normally denoted).The 3 extensions are then individually discussed in light of cosmological scenarios, where the different cosmological eras are used to constrain the form of the f function. In particular for f(T) also the energy conditions of the singularity theorems are employed to determine the signs of some coefficients. While the subject is certainly not completely new today, the authors bring, in my view, some order in the scheme that gravitational physicists are following at the moment, with a clear and up-to-date discussion and comparison. A point that I find very good is the fact that they do not fail to discuss also the negative sides of each. In a time in which people try to propose a plethora of disparate models, having someone discussing how some of them are not viable is healthy and sobering. This point could be improved, by bringing even more evidence for the problems of the non-metric approaches, or the lack of Lorentz invariance of others. However, things can always be improved, so I am not going to require the authors to do this. Just suggesting the possibility. Maybe in a further paper.

In the present one, whether or not they would like to bring more support for their findings, I would only ask to take care a bit of the English: the paper is generally clear, but sometimes, some sentences have minor things (like misplaced commas) that, while not too bad, nevertheless still make reading a bit slow in a few places.

Comments on the Quality of English Language

While overall very clear, it necessitates, in my opinion, a minor check (there are misplaced commas and ill-ordered verbs that sometimes make one re-read the sentence twice, even if, I repeat, the clarity is not disturbed much).

Author Response

Reply to the report of referee-2:

We would like to salute the referee, not for accepting the manuscript for publication, but for his graceful, humble, modest and sober review report, which is practically rare in these days. The manner in which he asked for some modifications is simply an act of a wonderful gesture which blooms only with wisdom. This is a lesson to learn.

In any case, we have tried to improve the issues mentioned by the reviewer (with updated citations) focusing on the degrees of freedom, Lorentz invariance, strong coupling issue of  F(T) gravity, and to some more detail to the recent findings in connection with the pathology of non-linear extension of symmetric telleparallel gravity F(Q) theory. These may be found in italics in the third paragraph of the introduction, first paragraph of section 3.2, the last paragraph before concluding remarks and in the concluding remarks. We have also sincerely gone through the text and made required language corrections, removing unnecessary commas. Some typos have also been taken care of.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Second Referee Opinion on the paper: Reconstructing modified and alternative theories of gravity Dalia Saha, Manas Chakrabortty and Abhik Kumar Sanyal  Universe 2770060

 

               The revised version of the paper Reconstructing modified and alternative theories of gravity Dalia Saha, Manas Chakrabortty and Abhik Kumar Sanyal is better. However, in many points it still needs corrections and improvements. The details are following:   regarding my point 1 and 2                  The authors explained their idea in a response to the reviewer but did not modify the first paragraph which specifically mentions FLRW UNIVERSE. I maintain my opinion that this paragraph is unacceptable in its current form. This paragraph absolutely requires modification and the authors' explanations for the reviewer are a good basis for making these changes.   regarding my point 4                  This was clearly written in the response to the reviewer. But this is not clear from the text of the work (even in its current form). A comment like the one in the response to the reviewer is necessary.   regarding my point 5                  Unfortunately, the first part of my statement at this point actually disappeared. Nevertheless, the authors understood my objection quite accurately, with the exception of: "However, it appears the referee is trying to state that the modified or alternative theories MAY NOT (NOT cannot) have Friedmann-like solutions" and this difference between MAY NOT and CAN NOT is important.                Again, the authors explained this issue in a response to the reviewer, while such a comment in the text is necessary   regarding my point 6   The statement in the text IS NOT SUFFICIENT because what the authors wrote in response to the reviewer is missing in the text: “modified and alternative theories should be treated as viable only if these theories admit Friedmann-like solutions in the radiation and early matter dominated eras.”   regarding my point 7                      I am convinced that a brief discussion of Palatini formalism, and in particular a description of the differences between it and the authors' approach and the resulting consequences, is necessary               

As for the authors' objections to my statement:

“In my opinion, all these points must be corrected, improved and clarified before the paper can be accepted to any journal”                      It was a polite statement that in my opinion these changes are necessary before the work will be suitable for publication anywhere. If the authors prefer to be more explicit, it was equivalent to saying "in my opinion without making these changes, the work is not suitable for publication in any journal"                  In my opinion, all the above points must be corrected, improved and clarified before the paper can be accepted for publications. Without these changes, the work is not suitable for publication.

 

Comments for author File: Comments.pdf

Author Response

Reply to the referee’s report and subsequent modifications:

We have now modified the manuscript as suggested by the referee. In the following the list of modifications may be found.

Points 1 &2: These have been included in the first paragraph of the introduction, in italics.

Point 4. We have now included it at the beginning of subsection 3.2, in italics.

Point 5 and 6. These have been included at the beginning of section 3, in italics.

Pont 7. We have also added a brief discussion of Palatini formalism in the new subsection 3.4, together with some additional citations.