Analysing Hubble Tension and Gravitational Waves for f(Q,T) Gravity Theories

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In this paper, the authors consider the resolution of the Hubble tension problem based on the modified f(Q,T)-gravity theory. Several types of f(Q,T)-gravity theories were considered. The presented analysis of modern observational data showed that these modifications of gravity theory reduce the Hubble tension.

Comments:
1. Despite the fact that the authors in their conclusion define the analysis of the CMB data as the result of future work, a question arises about the correctness of the proposed modifications of the theory of gravity in explaining the observed anisotropy and polarization of the CMB, since the metric (15) of a homogeneous and isotropic space-time is considered.
If the observed anisotropy and polarization of the CMB is associated with the influence of cosmological perturbations arising at the inflationary stage, then it is necessary to assess the possibility of compliance of the modified theories of gravity under consideration with modern observational constraints.
2. Also, do the proposed types of the modified gravity theories correspond to the modern tests in the Solar System?

After supplementing the text of the article with comments on these topics, I can recommend this article for publication.

Author Response

Comment 1:  Despite the fact that the authors in their conclusion define the analysis of the CMB data as the result of future work, a question arises about the correctness of the proposed modifications of the theory of gravity in explaining the observed anisotropy and polarization of the CMB, since the metric (15) of a homogeneous and isotropic space-time is considered.
If the observed anisotropy and polarization of the CMB is associated with the influence of cosmological perturbations arising at the inflationary stage, then it is necessary to assess the possibility of compliance of the modified theories of gravity under consideration with modern observational constraints.

Author's Reply: We completely agree that evaluating the models against the observed CMB anisotropy and polarization is essential. Because our current study focuses strictly on the background FLRW metric to address late-time expansion and the $H_0$ tension, it cannot account for the cosmological perturbations seeded during inflation. We have added a paragraph to the Conclusions section explicitly acknowledging this limitation. We emphasize that deriving the complete linear perturbation equations for $f(Q,T)$ gravity and interfacing them with Boltzmann solvers to extract the CMB angular power spectra is the mandatory next step for full observational compliance. Kindly see the section 4.

Comment 2:  Also, do the proposed types of the modified gravity theories correspond to the modern tests in the Solar System?

Author's Reply: We have added a discussion to the manuscript in section 6, acknowledging that the non-minimal couplings in our proposed models alter effective gravitational interactions. We note that these models must either adhere to stringent parameterized post-Newtonian (PPN) bounds or rely on local screening mechanisms to remain viable on astrophysical scales.

 

Please see the attachment.

 

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Please refer to the report

Comments for author File: Comments.pdf

Author Response

Please see attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have amended the text of the paper in accordance with previous comments. 

Nevertheless, I draw the authors' attention to the text added as a comment on the second question in conclusion:
"The functional forms analyzed here introduce non-minimal couplings between the non-metricity scalar and the trace of the energy-momentum tensor, which can effectively alter the gravitational coupling and potentially mediate fifth forces. To comply with modern Solar System constraints—such as those derived from Cassini tracking and planetary perihelion precession—the parameterized post-Newtonian (PPN) limit of these specific f(Q,T) models must be rigorously evaluated. For these theories to simultaneously drive late-time cosmic acceleration and satisfy local weak-field bounds, the parameters governing the modifications must either be highly suppressed on small scales, or the theory must naturally exhibit a screening mechanism in high-density environments to dynamically restore General Relativity."

I believe that in the absence of references to previous research or direct analysis of the issues raised, these claims are not sufficiently substantiated. Thus, in my opinion, it is necessary to at least add relevant references to current research in the field of the fifth force, post-Newtonian formalism and screening mechanisms for the case of f(Q,T)-gravity.

After these corrections are made, I will be able to recommend the article for publication.

Author Response

Dear Editor,
In the following we present the list of changes made in our manuscript: “Analysing Hubble Tension and Gravitational Waves for f(Q, T) Gravity Theories” by Aritrya Paul, Shreya Banerjee after the referees’ suggestions and advices. We thank the referee for his/her constructive and enlightening comments and for his/hercrucial clarifying points. Along these lines we performed a modification of our manuscript.
REFEREE COMMENT 1 : Nevertheless, I draw the authors’ attention to the text added as a comment
on the second question in conclusion: ”The functional forms analyzed here introduce non-minimal couplings
between the non-metricity scalar and the trace of the energy-momentum tensor, which can effectively alter the gravitational coupling and potentially mediate fifth forces. To comply with modern Solar System constraints—such as those derived from Cassini tracking and planetary perihelion precession— the parameterized post-Newtonian (PPN) limit of these specific f(Q, T) models must be rigorously evaluated. For these theories to simultaneously drive late-time cosmic acceleration and satisfy local weak-field bounds, the parameters governing the modifications must either be highly suppressed on small scales, or the theory must naturally exhibit a screening mechanism in high-density environments to dynamically restore General Relativity.” I believe that in the absence of references to previous research or direct analysis of the issues raised, these
claims are not sufficiently substantiated. Thus, in my opinion, it is necessary to at least add relevant references
to current research in the field of the fifth force, post-Newtonian formalism and screening mechanisms for the
case of f(Q, T)-gravity.

AUTHORS REPLY FOR REFEREE POINT 1 : We have included some references in support of the
paragraph in the conclusion section (section 6, page-24) in the text.

AUTHORS FINAL COMMENT:
We thank again the referee for his/her useful comments and suggestions.
We hope that the revised version is now suitable for publication.
Sincerely Yours,
The Authors