Reflections on the Covariance of Modified Teleparallel Theories of Gravity
Round 1
Reviewer 1 Report
In this article, the current status of the Lorentz covariance in teleparallel and modified teleparallel theories of gravity is reviewed in detail. The discussions should be important and the contents might be helpful for the related future works. Hence, this paper could be worthy of being published if the following points are reconsidered.
1. There exist the past review article in terms of the so-called $f(T)$ gravity with T the torsion scalar teleparallelism in the literature. By comparing with these preceding studies, the new ingredients and significant progresses of this work should be stated more explicitly and in more detail. Namely, the differences between this paper and the past ones should be described in more detail and more clearly.
2. Naively, the covariance of modified teleparallel gravity theories is a pure mathematical issue and therefore its existence and property could be determined once the action of the theories is described. Indeed, however, there are still several issues to be addressed, particularly regarding to the coupling of the antisymmetric part of the equations of motion of modified teleparallel to spinorial sources. What are the main reasons why such uncertainities could be exist?
3. Through the considerations about the inheritance of a remnant symmetry group of local Lorentz transformations, is it possible to any new viable condition
of $f(T)$ gravity as an alternative gravity theory to general relativity?
4. Finally, it is recommended that the wordings and grammar of English should be rechecked throughout the present manuscript.
Author Response
REPLIES/COMMENTS TO THE REVIEWER 1
Below, you can fi nd in bold letters our replies/comments in relation to the questions raised by the reviewer.
1. As a matter of fact, yes there exist a couple of reviews in the literature concerning f(T) gravity. However, the subject of the non-covariance under the Lorentz group was scarcely (and non-systematically) covered in them. It is our intention in this paper to gather the two main points of view (the so called covariant formulation and the remnant symmetries approach), and to critically discuss them. In this sense we consider our paper original, and different from those existing in the literature.
2. It is unclear the procedure through which matter is coupled to the tetrad in modi fed teleparallel theories, mainly because it is expected that the spin connection also plays a role on that, but its choice is still matter of debate. The ambiguity in this choice would be the main source of uncertainty of such coupling.
3. If the question alludes to the fact if whether or not the remnant group could help to select speci fic f(T) functions, the answer is no. The remnant symmetry is a property of the spacetime, it is only an on-shell symmetry, and is not related to the speci c form of the function f(T). For instance, the tetrads given in Eqs. (40) and (41) of our article are solutions of the f(T) equations for any ultraviolet f(T) function. The remnant group is characterized from the maximal n-CAF associated to this space (the 6-CAF given by (41) in this case), and it is the same for any f(T) deformation.
4. We improved the wording and grammar in some passages of the manuscript. All the changes are in red in an additional file.
Please accept our best regards,
Sincerely yours
The authors.
-------------------
List of changes:
-First paragraph of introduction: "symmetry group related WITH"
was changed to "symmetry group related TO THE FREEDOM OF BOOSTING OR
ROTATING"
-Second paragraph of introduction: "Early attemps....ARE considered"
was changed to "Early attemps....WERE considered"
-Also at the end of that second paragraph: "associated WITH the
metric" was changed to "associated TO the metric"
-In the middle of the third paragraph of intro: "drop the assumption of
the Weitzenbock...FOR a more", it should say "drop the assumption of the
Weitzenbock...IN FAVOR OF a more".
-"does no depend" -> Before Eq.17.
-"will enters" -> on chapter 4.
-"This is so because de 1-form" -> at the end of page 9.
-After Eq.48, it was changed from "outmost" to "utmost".
-Pag. 8, there was a "However" in upper case with a comma before. We put a dot and changed a "However" to "But".
-In Eq. (51), it was clarified that there isn't any summatory in alfa and beta.
-We added Ref.28 and a short text before Eq.37
-We added Ref.33 and a short text in line 208
Author Response File: 
Author Response.pdf
Reviewer 2 Report
In this manuscripts the authors present a critic review about some aspects of the Lorentz gauge symmetries in the so called f(T) theories.
It is a well-written, in-depth work, that I recommend for publication on Universe.
As singular minor point I suggest that the authors discuss with some details the importance of f(T) gravity in cosmology, where there is a large, renewed interest about these theories.
Best Regards
Author Response
REPLIES/COMMENTS TO THE REVIEWER 2
Below, you can find in bold letters our replies/coments in relation to the questions raised by the reviewer.
REVIEWER 2
As singular minor point I suggest that the authors discuss with some details the importance of f(T) gravity in cosmology, where there is a large, renewed interest about these theories.
Even though it would be nice to discuss with more detail several other aspects of f(T) gravity, it wasour intention to focus on the non-covariance of f(T) under the Lorentz group. This is a particularly technical aspect of f(T) gravity which is not commonly discussed in the literature. Undeniably, cosmological models have had an starring importance within this framework (actually, the firsts papers in the fi eld explored cosmological consequences of these theories), and nowadays they are certainly playing an important role in the observational aspects of f(T) gravity. However, as the number of publications unceasingly grow up, technical as well conceptual issues are not so popular. It was our aim to make a modest contribution in this direction, by critically discussing the two frequent (and, in a way, opposite) approaches to the Lorentz covariance problem.
Nonetheless, the importance of cosmological implications within the f(T) framework is mentioned several times in our article; for instance, in the last paragraph of the introduction, at the end of the paragraph preceding Eq. (34), and in the one following Eq. (35).
Please accept our best regards,
Sincerely yours
The authors.
Reviewer 3 Report
The authors reviewed the study status of the Lorentz covariance issue in the teleparallel gravity theories and beyond and revisited the remnant Lorentz gauge symmetries within f(T) gravity. The topic is of sufficient interest to certain readers of the journal. The analyses are self-consistent and the presentation is well expressed. Therefore, I feel the article is available for publication. Before that, I invite the authors to address the following optional comment.
While the current manuscript was prepared in theoretical perspective, it would be nice to add a discussion on connecting with cosmological implications, namely the constraints of such type of gravity theories can be arisen from effective field theory approach (https://arxiv.org/abs/1803.09818) as well as gravitational wave astronomy (https://arxiv.org/abs/1801.05827).
Author Response
REPLIES/COMMENTS TO THE REVIEWER 3
Below, you can find in bold letters our replies/coments in relation to the questions raised by the reviewer.
REVIEWER 3
While the current manuscript was prepared in theoretical perspective, it would be nice to add a discussion on connecting with cosmological implications, namely the constraints of such type of gravity theories can be arisen from effective field theory approach (https://arxiv.org/abs/1803.09818) as well as gravitational wave astronomy (https://arxiv.org/abs/1801.05827).
The articles suggested by the reviewer are interesting, but we feel that they are not in close connection with the points we are focused on. Our article tends to critically discuss the specific subject of the non-covariance of f (T) gravity in general, not in relation to cosmological models and gravitational waves in particular. To keep track of the recent advances within the field is clearly out of the scope of our article.
Please accept our best regards,
Sincerely yours
The authors.
