Teleparallel Robertson-Walker Geometries and Applications
Round 1
Reviewer 1 Report
1. The first 6 pages are almost a reproduction of the first 8 pages of Ref. [7]. The authors of Ref. [7] retain copyright and one of them is author in the present manuscript. Such self-plagiarism should not have taken place.
2. From a physics point of view, the manuscript is poorly written: No physics interpretation of whatsoever. Moreover, the work is not well motivated.
3. The manuscript is not self-contained: Some notions introduced by the authors are not familiar even to those who work on F(T). The authors have to clarify or define the special notions as the Cartan-Karlhede algorithm.
4. Page 2, Lines 34, 35: First of all, write the RW equations. There is confusion in the sentence: "We note that k, which is the spatial curvature in the RW metric ... in 4-space it is part of the torsion scalar". The authors are requested to re-write it.
5. Pages 4, 6, 5: What's a "proper frame"? How this is related to the term "good frame" that some authors use? The authors are requested to comment on the sentence "Hence, there are no ‘good’ or ‘bad’ tetrads in f(T) gravity, there is no-frame dependence, as long as one abandons the strong imposition of zero spin connection (the peculiar non-diagonal, ‘good’ tetrads were just a naive way of being consistent with a vanishing spin connection)". See Conclusions section of Class. Quantum Grav. vol. 33 (2016) 115009 (http://dx.doi.org/10.1088/0264-9381/33/11/115009).
6. How were Eqs. (10) & (12) derived? Justify without deriving the equations.
7. Page 5, Line 130: "connection pair (4) and (10)" should read "connection pair (4) and (12)".
8. Section 5.1. Stability Conditions: The authors are requested to re-write this section explaining what do they mean by stability? Stability analysis is usually performed via a perturbation approach of the metric and other fields or via a dynamical system analysis.
Author Response
"Please see the attachment."
Author Response File: 
Author Response.pdf
Reviewer 2 Report
After reading the article I have the following comments:
1. In cosmology, the metric of homogeneous isotropic universe is usually called the Friedmann-Robertson-Walker or Friedmann–Lemaître–Robertson–Walker metric.
2. On page 6 line 153 the statement is incorrect: "We recall that if T = const, then the theory reduces to GR and we obtain teleparallel analogues of the solutions in GR."
Under condition T=const, from dynamic equations for k=0 there follows only one type of solutions for the teleparallel equivalent of General Relativity (TEGR), namely de Sitter solutions with H=const.
It is also unclear how these solutions can be obtained from equations (14a)-(14b) for T=const and function (18) taking into account T=6H^{2}. In my opinion, this statement needs to be explained in more detail.
3. Ð age 6 line 155: The condition of the constant state parameter \alpha=const implies only one type of ideal barotropic fluid, while for realistic cosmological models several types of material fields are considered (at least baryonic matter and radiation).
4. Ð age 9 section 5: The authors consider the power-law dynamics of the expansion of the universe. This case allows one to describe only one stage of the evolution of the universe (for a specific value of n), while a correct cosmological model should contain at least two stages of accelerated expansion of the universe and the stage of predominance of radiation and matter as well.
5. Ð age 10 subsection 5.1.1: Condition n<0 implies contraction of the universe instead of expansion. What stage of the evolution of the universe the authors considered in this case?
Condition 1/3<\alpha\leq1 implies the stiff matter only and the absence of baryonic matter \alpha=0 or radiation \alpha=1/3, which makes the solutions incorrect for the current stage of the evolution of the universe.
6. Ð age 11 lines 232-233: For the case of expansion of the universe n>0, conditions -1<\alpha\leq-1/3 and -2/3<\alpha\leq-1/3 imply exotic fields with negative pressure. There is no physical interpretation of these fields in the article.
Also, due to the absence of baryonic matter and/or radiation, these solutions can only correspond to the first inflation of the early universe (n\gg1), but due to the lack of evolution of the state parameter, as well as due to power-law dynamics, there is no exit from inflation in this model.
For the more general case -1<\alpha\leq1, due to power-law dynamics a\sim t^{n}, it is also possible to describe only one of the stages of the universe's evolution.
Thus, in my opinion, the model proposed in the article cannot be considered as a correct cosmological model.
7. As an illustration of the proposed approach in this article, I suggest that the authors consider a correct cosmological model with a different type of dynamics of the universe's expansion.
Author Response
"Please see the attachment."
Author Response File: Author Response.pdf
Reviewer 3 Report
After first studying the k = 0 models and, in particular, writing their governing field equations in the proper form, authors in teleparallel Robertson-Walker (TRW) geometries then studied their late-time stability with respect to perturbations in k in both the cases of a vanishing and non-vanishing effective cosmological constant term. As an illustration, they considered both quadratic F(T) theories and power-law solutions.
All teleparallel geometries that are invariant under the entire G_6 Lie algebra of Robertson-Walker affine symmetries have been shown. In the circumstances of non-zero k, they have discussed and explained their properties. For the F(T) class of teleparallel TRW spacetimes, they have specifically computed the geometries in the appropriate coframes and displayed the correct field equation. The governing field equation was then written as an ordinary differential equation after they studied the features of the resulting cosmological models with k = 0.
I recommend accepting the article in its current format.
Author Response
"Please see the attachment."
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
I am satisfied with the author's amendments: The overall presentation has been improved and more references have been added. No self-plagiarism detected.
Author Response
"Please see the attachment."
Author Response File: Author Response.pdf
Reviewer 2 Report
1. I believe that the authors have the right to their own interpretation of the name of the metric (5).
However, in my opinion, the author's name for the metric (5) corresponds to neglect of the contribution of Friedman and Lemaître in defining this metric of a homogeneous and isotropic universe.
For this reason, it would be more clear to cite some work in modern cosmology in which the metric (5) was called the Robertson-Walker metric.
This comment is not critical and can be considered as a recommendation.
2. In work [1] it is stated that for T=const the tetrad equations are reduced to the ordinary Einstein equations with a cosmological constant. In this case, different GR-like solutions correspond to different space-time metrics, while the work considers cosmological models based on metric (5). When applied to the FLRW space-time for T=const and k=0, this leads to de Sitter solutions only, which I wrote about in detail in the first comments to the work.
For case n\neq0, condition T=const and equation (16) lead to two possible other solutions, however, these solutions are special cases of GR-like solutions corresponding to metric (5).
In my opinion, it should be noted that condition T=const implies particular solutions to the equations of dynamics for metric (5), and it does not correspond to all GR-like solutions.
3. Substituting expression p=\alpha\rho with different coefficients \alpha corresponding to baryonic matter \alpha=0 and radiation \alpha=1/3 into energy-momentum conservation equation (16) leads to different values of the parameter n for matter and radiation in expression for the Hubble parameter H=n/t.
Thus, the density of matter and radiation changes over time according to different laws, corresponding to different values of coefficient n.
Therefore, by virtue of equation (16), I think it is incorrect if in cosmological model the radiation density and the matter density evolve by the same law.
For this reason, in previous comments, I wrote that a model with a Hubble parameter of H=n/t for a specific value of n corresponds to only one material field, and not several ones (in this case, it does not correspond to a mixture of non-interacting matter and radiation).
(Lines 253-254) It is not clear how the sum of two components with constant state parameters (a non-interacting mixture of dust and radiation) can be considered as a field with a variable state parameter.
It is necessary to explain in more detail or add literature references to the text.
Also, when including a scalar field in the model, it is necessary to determine the type of evolution of field \phi=\phi(t) and its potential V=V(\phi) for the Hubble parameter H=n/t in explicit form, which is missing in subsection 5.1.4.
Will the potential of the scalar field V=V(\phi) have a clear physical interpretation from the standpoint of field theory for this model?
4. It is necessary to indicate in more detail how the scale factor a(t) corresponding to the Hubble parameter H=n/t changes for n>0 and n<0. How is cosmic time t determined? Does it take a positive t>0 or negative t<0 values?
6.If the proposed model describes the second stage of the accelerated expansion of the universe in the present era, the question arises: how do the obtained restrictions on parameters n and \alpha correspond to the observed rate of accelerated expansion of the universe?
5. Thus, I still consider the cosmological model proposed by the authors to be insufficiently physically motivated and I propose to take into account the comments above.
Author Response
"Please see the attachment."
Author Response File: Author Response.pdf
