Contemplating the Fate of Modified Gravity

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

1. The author's give a general review of existing approaches and a panoramic picture of the current state of modified gravity, but the author should focus on giving his own ideas or methods for improvement in respect of these approaches.

2.In line 358: ...a very radical modification of gravity for quantization...,

the author should give the corresponding ideas and  methods and some examples.

3. In line 353...still miss something truly important.... , the author 

should give the corresponding explanation of  something truly important.

4. ...some independent theory of studying  models with a strong coupling... 

the author should give the corresponding explanation of the  theory  and some examples.

5.There are some improper, unclear expression and colloquial expression in the language of the manuscript. The author is suggested to modify the language of the manuscript in detail.

Comments on the Quality of English Language

There are some improper, unclear expression and colloquial expression in the language of the manuscript. The author is suggested to modify the language of the manuscript in detail.

Author Response

Please see the attachment and the submitted new version of the manuscript.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

In their paper: "Contemplating the fate of modified gravity" the authors make an sketchy classification of modified gravity and add some considerations, according to their experience and motivations, concerning the future of their area of research.

This work is neither a regular paper nor a review. I would say that it seems more as an essay on philosophy of science that reads as a stream of consciousness. Although, it could serve as motivation for a guideline of future work of practitioners of the field of modified gravity, in my opinion it seems too simplified for being of any interest for readers of the journal Universe unfamiliar with this research.

In this sense, I will recommend that the authors would include a table or list with a classification of modified gravity models more popular today, including the lagrangian and field equations for the simpler implementation of these models, the motivation for these generalizations of General Relativity and the predictions that could be tested experimentally or that are relevant to solve problems in cosmology. This would be useful to guide the reader in the vast forest of theories.

The authors make the statement that the lack of a guiding principle is one of the reasons we are lost in the swampland of the many proposals for modified gravity models in the literature.

In connection with this it could be discussed that Einstein was also lost for some years in the search of the equations of GR. In the so-called Entwurf theory of 1913 published with Grossmann as coauthor they were still dubious about the tensor that should be included in the left-hand side of the field equations and that should be proportional to the stress-energy tensor in the right-hand side.

Grossmann suggested that the Ricci tensor could play such a role. But they wrote the field equations as R_mu,nu=k * T_mu,nu and, therefore, the Newtonian limit was not recovered and this proposal was rejected. See: https://einsteinpapers.press.princeton.edu/vol4-doc/324

Only in 1915, Einstein realized that the equation should be generally covariant and this allowed him to write the field equations correctly and to deduce the anomalous precession of Mercury from them , which was really the key point in convince him that this version of the theory was right. Over all those years the guiding motivation of Einstein was the correct derivation of this anomaly.

As N. T. Roseveare says in his book "Mercury's Perihelion from Le Verrier to Einstein":

"I think that the reason for … the general neglect of the perihelion of Mercury as an anomaly to be explained by any new gravitational theory [in 1913] was that Seeliger’s hypothesis was being taken very seriously… Since it was felt by both Einstein and Nordstrom that no empirical argument existed beyond the light deflection predictions, one can only assume that the perihelion motion of Mercury was not considered to be anomalous and that the prevailing hypothesis explaining it, Seeliger’s hypothesis, was valid."

Seeliger was an austro-hungarian astronomer that has hypothesized the existence of a mass ring around the Sun:

https://dwc.knaw.nl/DL/publications/PU00012648.pdf

The theory of Seeliger was believed by most astronomers. So, Einstein was almost alone in thinking that there was an anomaly that required a new gravity theory.

A similar situation, according to some authors, is happening today with the dark matter and dark energy of standard cosmology. This is motivating a lot of research in modified gravity models that could produce alternatives cosmologies. One example, is tensor-vector-scalar gravity or TeVes of Jacob Bekenstein, very briefly commented by the authors of the present essay.

Another popular model developed with the objective of dispensing with dark matter is the Scalar-Tensor-Vector theory of John Moffat and collaborators. This theory predicts many phenomena that would, in principle, require dark matter in standard cosmology but it fails in the prediction of different arrival times for electromagnetic and gravity waves in the event GW170817 (PRD 2018, 97, 041501). Recently, it has also been shown that the observed velocity dispersion profile of the galaxy Dragonfly 44 do not agree with the predictions of MOG The Astrophysical Journal 2019 884, L25. arXiv: 1909.07978v1.

These models are interesting because they address a phenomenological problem, i.e., dark matter phenomena, and they are, at least, falsifiable by observations.

The search for an unified field theory in the classical sense that would encompass both the gravitational and the electromagnetic interactions was a strong driving force for many attempts to extend General Relativity by Einstein himself as well as many other physicists including Weyl, Schrödinger, etc. Although this approach is discredited and replaced by more modern quantum field models such string theories, I think that some words about this could be said. For a good review about these extensions see: https://link.springer.com/article/10.12942/lrr-2004-2

Adding torsion to the structure of space-time is also a popular approach with a long tradition. Some words are said about this by the authors of this paper but I think it would be necessary to link the present efforts to the Einstein-Cartan theory of 1922 which it is the most simple Poincaré gauge theory. For a nice review of the many options for incorporating torsion into the picture of gravity see the review by R. T. Hammond, Rep. Prog. Phys. 65 (2002) 599–649.

When there were little experimental evidence on the validity of GR, save for the three classical tests on light bending, perihelion precession and gravitational redshift, still flourished alternatives to GR that completely replaced the field equations and main tensors of the theory. For example, the so-called New General Relativity formulated in Weitzenböck space-time with zero curvature and all the physics derived by torsion instead. This comes again from a model from Einstein formulated 1928 (See the paper of Hayashi-Shirafuji, PRD 19(12), 1979, pp. 3524-3553).

Other teleparallel versions of GR are still proposed: Gen.Rel.Grav. 36 (2004) 101-110. With the many recent verifications of standard GR: detection of gravitational waves, geodetic effect, frame-dragging, concordance cosmology, etc, these radical alternatives to GR seem very unlikely but I think the authors could add a paragraph about this and in favour of modified gravity as commonly understood, i. e., models build up upon the main structure of standard GR.

I hope that these suggestions could help the authors to improve their paper. In any case, I think that, after proper revision, its publication in Universe is recommended.

Comments on the Quality of English Language

Minor editing of English language required

Author Response

Please see the attachment and the submitted new version of the manuscript.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

1. The manuscript contains an accessible review to the subject. It is clearly written and it should give useful information to the interested readers.

2. The manuscript is clearly written and provides a good overview of the approaches followed in recent years in order to solve the difficulties found in the study of relativistic cosmology. The references cited constitute a good guide to the pertinent material.

Author Response

Please see the attachment and the submitted new version of the manuscript.

Author Response File: Author Response.pdf