Generic Modification of Gravity, Late Time Acceleration and Hubble Tension

Round 1

Reviewer 1 Report

This paper is very-well written, and the model give rise to late-time acceleration, as well as resolving the Hubble tension, one of the problems which plague the (Lambda)CDM model. The paper can be accepted, but the authors should give a more clear explanation of a disformal transformation in section 3.0.1. Also the labeling of the sections in section 3 should run from 3.1-3.5 rather than 3.0.1 to 3.4.

Author Response

Dear Reviewer,

Thank you for pointing this out. We have done the following changes:

(1) The numbering of third section,

(2) We have added an explanation for the disformal transformation. 

Thank you

Regards

Reviewer 2 Report

Authors suggested interesting way to solve several problems of modern cosmology. Introducing specific interaction between dark and baryon matter allows to explain late-time cosmic acceleration without including any exotic fluid (dark energy). Authors showed that considered scenario is consistent with observational data and in a case of polynomial representation for scale factor resolve Hubble tension problem. 

I think that paper can be published in journal but some moment about SNe should be clarified. Why authors used Pantheon+MCT SnIa data with six Hubble rate data points for z<1.5 and 15 points for z>1. For example Union2 compilation consists of 580 SNe samples and maybe analysis of this dataset is better from statistical point of view?  

Author Response

Dear Reviewer,

Thank you for your valuable comments.

The data that we have used effectively compresses the information of the 1050 SN1a at z<1.5 that take part of the Pantheon compilation (which includes 740 SN1a of the JLA sample), and the 15 SN1a at z>1 of the CANDELS and MCT program obtained by HST. It has been shown that this compressed data is more robust and also give similar results if one take full SN1a sample such as Union2 or Pantheon.

Thank You

Regards

Mohit

Reviewer 3 Report

This manuscript describes the implications of a large-scale modification of gravity.

Such a treatment does not call for the need of further degrees of freedom: using the

coupling of baryonic matter and dark matter in the Einstein frame, this theory is capable

of reproducing a late time acceleration and provides a probable solution for the so-called

Hubble constant tension.

 

The manuscript is well-written and I would recommend it for the publication in your journal 

after addressing some extra points that I list below:

 

1) MAIN COMMENT

It is interesting how the authors parametrized the function R(a) both in a polynomial form (Section 

3.3) and an exponential form (Section 3.4). However, there is another form to parametrize R(a) 

that could be tested in this work: namely, a_tilde=(a0_tilde/(1+z_tilde)^eta), a=(a0/(1+z)^eta), 

where the main difference with the polynomial form is that only the first term of Equation (31) 

is kept and the denominator is elevated to the power of eta, being eta an evolutionary parameter.

Such a functional form has been investigated directly on the value of the Hubble constant H0

in the paper:  M. G. Dainotti et al 2022 Galaxies 10(1) 24.

 

It would be interesting, in light of the theoretical discussion and the probes used in this paper,

to plot the contours for the eta and h_tilde parameters, expanding the contents of Section 6.

 

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2) EXPANDING THE REFERENCE LITERATURE

Despite being the basic literature sufficient to the purposes of the paper, it would be advisable to

expand further the Section 2 about the Hubble tension overview.

> The paper M. G. Dainotti et al 2022 Galaxies 10(1) 24 should be cited since it is the expansion of 

the contents seen in M. G. Dainotti et al 2021 ApJ 912 150: in the subsequent paper, the parameter

space has been enlarged up to two and the BAOs have been added to Supernovae Ia, confirming the 

decreasing trend of H0 with redshift.

 

Together with the Early or Late Time modifications/transitions as solutions to the Hubble constant

it would be better to cite also the most promising future probes that can cover redshift ranges far

beyond the detection limit of Supernovae Ia and represent reliable standardizable candles. In this case, 

the following papers that discuss their applications and their correction for redshift evolution are suggested:

 

Quasars:

> Bargiacchi, G., Risaliti, G., Benetti, M., Capozziello, S., Lusso, E., Saccardi, A. and Signorini, M., 2021, Astronomy & Astrophysics, Volume 649, id.A65, 10 pp.

> Bargiacchi, G., Benetti, M., Capozziello, S., Lusso, E., Risaliti, G. and Signorini, M., 2022, Volume 515, Issue 2, pp.1795-1806.

> Łukasz Lenart A., Bargiacchi G., Dainotti M. G., Nagataki S., Capozziello S., 2022, arXiv e-prints, p. arXiv:2211.10785

> M. G. Dainotti et al 2022 ApJ 931 106

 

GRBs:

> M G Dainotti, A Ł Lenart, A Chraya, G Sarracino, S Nagataki, N Fraija, S Capozziello, M Bogdan, MNRAS Volume 518, Issue 2, January 2023, Pages 2201–2240

> M G Dainotti, V Nielson, G Sarracino, E Rinaldi, S Nagataki, S Capozziello, O Y Gnedin, G Bargiacchi, MNRAS Volume 514, Issue 2, August 2022, Pages 1828–1856

> M. G. Dainotti et al 2020 ApJ 904 97

> M. G. Dainotti et al 2016 ApJL 825 L20

> V. F. Cardone, M. G. Dainotti, S. Capozziello, R. Willingale, MNRAS, Volume 408, Issue 2, October 2010, Pages 1181–1186

> M. G. Dainotti, V. F. Cardone, E. Piedipalumbo, S. Capozziello, MNRAS, Volume 436, Issue 1, 21 November 2013, Pages 82–88

> Shulei Cao, Maria Dainotti, Bharat Ratra, MNRAS, Volume 512, Issue 1, May 2022, Pages 439–454

> Shulei Cao, Maria Dainotti, Bharat Ratra, MNRAS, Volume 516, Issue 1, pp. 1386-1405

> M. G. Dainotti, G. Sarracino, S. Capozziello, PASJ, Volume 74, Issue 5, October 2022

 

Other promising probes:

> M. G. Dainotti et al 2022 ApJ 938 41 (GRB-SNe)

Author Response

Dear Reviewer,

Thank you for your valuable comments. We have taken into account your suggestions in our modified version of manuscript.

 

Thank You

Regards

Mohit

Reviewer 4 Report

This is a nicely prepared paper that I am happy to recommend for publication, perhaps after some minor edits.

I do have a few concerns that the authors might wish to address before finalizing their manuscript, should they choose to accept my suggestions.

1. In accordance with Eqs. (2) and (11), both the conformal scaling and the additional shift term in the metric are governed by the "dark matter" scalar field \Phi. Inevitably, I am left thinking that this truly is just Jordan-Brans-Dicke theory in disguise, which is known to be limited by stringent post-Newtonian constraints obtained mostly from interplanetary spacecraft observations. Could the authors comment on this?

2. Although eventually it becomes evident (I think) that they don't, in a few places I was almost left under the impression that the authors sometimes treat \tilde{g} as a separate tensor degree of freedom as opposed to something that is algebraically constructed from g and \Phi. Might be useful to remind the reader that you know what you are doing and help the reader make sense, e.g., of statements like the opening sentence of 3.1 (which, of course, is valid so long as the baryonic sector couples to \tilde{g}, not g, universally and minimally.)

3. A trivial notational convention issue but the use of capital R in (11) and onward confused me on several occasions, since R is also the Ricci tensor. A different letter (as opposed to just varying typography) might be very helpful.

4. It might be useful to stress that (28) is valid only because on the previous page, BM was presumed to be pressureless to begin with.

Well, this is pretty much it. I of course hope that I didn't miss some elephant in the room. (Bad papers are easy to reject. Good papers are much harder to referee, because one always worries of missing something critical.) I hope my comments prove useful. In any case, I think this paper deserves publication.

Author Response

Dear Reviewer,

Thank you for your valuable comments and suggestions. 

Response to your first comment:

In contrast to the Brans-Dicke theory, the main difference lies in the fact that the Dark matter (DM) interacting with baryons can result in cosmic acceleration, even if there are no sources of negative pressure or additional degrees of freedom beyond DM and ordinary matter. It is also important to mention that screening mechanism prevents the direct coupling between DM and ordinary baryon particles from violating the Equivalence Principle.

 

Response to your second comment: 

We have added a footnote to avoid any kind of confusion for the reader.

 

Response to your third comment: 

We have changed the symbol R to Y everywhere in our manuscript.

 

 

Response to your fourth comment: 

We have specifically write it down in the suitable place.

 

I hope this address all your issues.

Thank You

Regards

Mohit

Round 2

Reviewer 1 Report

The authors have addressed the points raised, and the paper may now be published

Author Response

Dear Reviewer,

We thank you for giving your precious time to go through our paper, and also for your suggestions.

 

Reviewer 2 Report

Authors answered on my questions and I think that paper can be published in present form

Author Response

Dear Reviewer,

We thank you for giving your precious time to go through our paper, and also for your suggestions.

Reviewer 3 Report

Dear Authors,

Thank you for submitting the new version of your manuscript. I am still concerned about the first suggestion I gave you in the first review. I was not able to find, in the manuscript, a plot - a computation or even a discussion about a parametrization of the a(a_tilde) parameter as a(a_tilde)=(a_0tilde)/(1+z_tilde)^alpha or the corresponding a=(a_0)/(1+z)^alpha.

Concerning the citations, I think they are properly reported now.

Thank you in advance for your patience and your effort in improving the manuscript according to my suggestions.

With best regards,

The reviewer

Author Response

Dear Reviewer,

We are thankful for your comments, and your suggestion to see the how does your parametrization: a(a_tilde)=(a_0tilde)/(1+z_tilde)^alpha will be helpful to address the Hubble constant problem. We find that this analysis using this parametrization should definitely be done, that is why in the conclusion of our modified version of paper we have kept that as our future agenda.

Thank You

Reviewer 4 Report

I reviewed the changes and find that the authors addressed all my previous (minor) concerns. I am glad that my suggestions proved useful and I am happy to recommend the paper for publication.

Author Response

Dear Reviewer,

We thank you for giving your precious time to go through our paper, and also for your suggestions.