Weak Gravity Limit in Newer General Relativity

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Review report for the paper titled "Weak Gravity Limit in Newer General Relativity" by Alexey Golovnev, Sofia Klimova, A.N. Semenova, and V.P. Vandeev:

In this paper the authors studies the weak gravity limit in new relativity theory. They propose a quadratic action in terms of the non-metricity tensor, adopting an approach based on the linearization of the resulting field equations around the simple Minkowski metric. The paper is interesting and is worth reading, needing some clarifications:

-the Introduction is insufficient and needs to be completely rewritten; the authors should explore and present the history of the present model;

-the authors should present the reasons for adopting the Symmetric Teleparallel Equivalent of General Relativity limit in this paper and the improvements generated by such a model;

-some missing citations should be introduced in the section 2 and 3; 

-section 6. ("Review of Pathological Models") is not clear from a theoretical point of view;

-the Conclusion section is insufficient and needs more arguments;

The authors should also consider the exploration of the parameter's space, considering the introduction of regionplots [https://reference.wolfram.com/language/ref/RegionPlot.html] or other reconstruction approaches. A numerical example should make the paper more readable. Hence, different numerical applications should be considered for the analytical results considered by the authors.

The main conclusion of the report is that the paper is interesting, having multiple drawbacks due to the writing style. The authors should partly rewrite the paper and introduce some numerical examples. 

Author Response

We thank the Referee for the positive assessment of our paper.

However, we find it hard to answer all the comments because we don't find many details in those. For example, it is not clear for us what precisely is "not clear from a theoretical point of view" in the Section 6. This section is included for completeness. It refers to models which can hardly be viable due to the issues in tensor and vector modes (either ghosts or other instabilities, or absence of gravitational waves). We give some details on the scalar modes' behaviour in those models.

"-the Introduction is insufficient and needs to be completely rewritten; the authors should explore and present the history of the present model;"

It's not clear for us, what is unsatisfactory in our introduction. As to the history, we have added several remarks on the birth of symmetric teleparallel approach to gravity, as well as a number of current directions of research with references.

"-the Conclusion section is insufficient and needs more arguments;"

This statement is not clear for us either. We have added several sentences though.

"-the authors should present the reasons for adopting the Symmetric Teleparallel Equivalent of General Relativity limit in this paper and the improvements generated by such a model;"

We do not adopt the case of STEGR. It is one of the possible models, and it is not interesting to study since it is indeed equivalent to GR. We study all other cases of the quadratic Lagrangian.

"-some missing citations should be introduced in the section 2 and 3;"

What citations are missing? We have put some citations regarding the Newer GR. In the Section 3, we have also added a citation to the classical paper on cosmological perturbations, even though it is a classical textbook material by now.

Finally, our work is purely theoretical and analytic. That's why we do not make any plots or numerics.

Reviewer 2 Report

Comments and Suggestions for Authors

The article studies the linearised field equations around Minkowski metric in Newer GR (General Relativity) where the action is in terms of the non-metricity tensor and 5 parameters (one of them related to the others in the weak field limit). The authors calculated the field equations in the weak gravity limit and examined the tensor, vector, and scalar sectors. They also explored the extra degrees of freedom as well as some pathological models. In the particular case of Symmetric TEGR (Teleparallel Equivalent of General Relativity) with specific choice of the 5 parameters in the action, the extra degrees of freedom are analyzed.

The manuscript is well-written and well-organized. The results are clearly presented. As a constructive criticism, I suggest improving the Conclusions section in order to summarize the main results obtained and the different cases shown. There is sufficient new material in this paper so it could be better exposed in the last section.

Author Response

Thank you very much for the very positive report. The Conclusions section has been expanded a bit.

Reviewer 3 Report

Comments and Suggestions for Authors

In the manuscript “Weak Gravity Limit in Newer General Relativity” the authors investigate the weak limit of linearised gravity within the quadratic symmetric teleparallel theory dubbed Newer GR. 

The goal of this work is valuable since it is of paramount importance to assess whether this limit recovers the familiar gravitational scenario, or whether there are any specific differences to be wary of. The authors produce a comprehensive analysis of this question, and identify some  caveats that they competently discuss.

The manuscript is well written an well organised. 

I thus find this work relevant and of interest for the community of cosmologists,  and thus recommend its publication in the journal Universe.

Author Response

Thank you very much for the nice and kind words.

Reviewer 4 Report

Comments and Suggestions for Authors

The authors in this paper analyze a symmetric teleparallel model, the so-called Newer GR, in the weak field limit around the Minkowski metric, which is based on a gravitational action linear in the nonmetricity scalar in which we keep four of the five free parameters of the theory. In particular, for a STEGR theory with an additional term of the gradient squared of the metric determinant, thanks to the usual cosmological perturbations of the metric, pathologies such as instabilities and the presence of ghost modes in the tensor, vector and scalar sectors have been studied, identifying which are the dynamic and physical modes through the study of the positive definiteness of the kinetic matrix. After a careful and rigorous analysis of the degrees of freedom of this model, the authors demonstrate the presence of three new dynamical degrees of freedom, and not one as previously claimed, in the scalar sector of perturbations. 

The article is very well written, clear and scientifically correct. The results are very well highlighted and the paper is well organized. It is only recommended to add some more references to the bibliography, since the field of symmetric teleparallel theories of gravity and its modifications is full of scientific papers, such as Phys. Rev. D \textbf{110}, no.10, 104028 (2024); arXiv:2503.08167v1 [gr-qc]].

After taking these little suggestions into account, the manuscript is suitable for publication in Universe. 

Author Response

Thank you very much. Some references have been added to the list.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The paper has been improved, and it might be published in the present form.