Measuring the Modified Gravitational Wave Propagation beyond General Relativity from CMB Observations

Round 1

Reviewer 1 Report

In this paper, the authors discussed the constraint on the primordial gravitational waves, if assuming the friction term exists in the propagation equation of GWs. By applying the recent CMB observations, the author derived the constraints on the amplitudes of PGWs and the parameters of friction term. The idea and calculation is interesting, and I have only small comments as belows:

(1) I suggest to change the title "...... from observations" to "...... from CMB observations"

(2) Recently, there are many works to discuss and constrain the friction terms of GW from the LVC collaboration (see for instance, 1909.10887, 2112.05728, 2108.10872), which should be comments at least in the papers.

(3) For the consistency relation used in Eq.(13), which is derived in the General Relativity framework. However, in the paper, it is in the modified gravity, I am not sure, whether or not it is still holden. Please clarify it.

Author Response

Dear reviewer，

Thank you for your comments. We enclose our reply as follows.

(1) We change the title "...... from observations" to "...... from CMB observations".

(2) We add some references and discuss them in line 27.

(3) The consistency relation in GR is nt=-r/8 in line 70 and the consistency relation in modified gravity is given by Eq. (14).

Please reconsider our paper for publication in Universe.

Yours sincerely,

Jun Li 

Reviewer 2 Report

In this paper the author studies the impact on the B-mode polarization power spectrum due to a modified friction term in the equation of propagation of gravitational waves during Inflation. The author parametrizes the departure from GR in that equation with a simple constant term, \nu_0, and puts some constraints on it and the tensor-to-scalar ratio r using data from BK18. My main concerns are the following: 

1) The author assumes that the underlying modified theory of gravity that rules the expansion of the universe in the inflationary phase only changes the tensor perturbations. The impact of the scalar perturbations is not considered in this analysis. In general, though, we expect modified gravity effects to have an impact on both, tensor and scalar perturbations, and also at the background level. This is what happens e.g. even in the original Brans-Dicke theory. More complicated models within the Horndeski family naturally lead to similar situations. I suspect that the simpified framework considered in this paper is not sufficient to obtain realistic and representative constraints on \nu_0 and r.  

2) In addition, the author fixes the 6 cosmological parameters to the values reported by the Planck collaboration. This could lead to important biases in the fitting results for the parameters \nu_0 and r. In order to obtain more robust results, the author should perform a joint fitting analysis using Planck + BK18 data, allowing all the parameters of the model to vary in the Monte Carlo run.

Other minor comments: 

3) Is P_h and P_t the same tensor power spectrum? If so, the author should use the same notation throughout the paper.

4) The formula below (4) is not numbered, and the notation employed in this expression should be better explained.

5) In formula (9), what is the superscript 0 of h_k^0?

6) The writing could be strongly improved. 

Comments (1) and (2) are particularly important. The author should argue in their reply why the results are significant and sufficiently general. At this point of the refereeing process I cannot recommend this paper for publication. 

Author Response

Dear reviewer，

Thank you for your comments. We enclose our reply as follows.

(1) The modified gravity may have an impact on both tensor and scalar perturbations. If all of the modified terms are considered together, it is hard to figure out the effects of the friction term. Here we parametrize the friction term only and investigate corresponding observable effects.

(2) We perform a joint fitting analysis using Planck + BK18 data, allowing all the parameters of the model to vary in the Monte Carlo run. The numerical results in Eq. (15) and (16) are changed.

(3) We use the same notation P_h throughout the paper.

(4) The formula below Eq. (4) is numbered, and the notation employed in this expression are explained.

(5) We explain the superscript 0 of h_k^0.

Please reconsider our paper for publication in Universe.

Yours sincerely,

Jun Li 

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

The author has addressed the points raised in my previous report. Although the constraints obtained for the friction term nu_0 maybe are not very representative of those that would be obtained in a general modified theory of gravity, I deem this paper deserves to be published. It is interesting to see the impact of the friction term on the power spectrum of B-modes and the impact on the constraints on the other parameters (e.g. r or A_t) when \nu_0 is allowed to vary in the Monte Carlo analyses. Maybe this last point could be mentioned in the abstract and further emphasized in the conclusions.

Author Response

Dear reviewer，

Thank you for your comments. We enclose our reply as follows.

We explore the impact of the friction term on the power spectrum of B-modes and the impact on the constraints on the other parameters (e.g. r or At) when ν0 is allowed to vary in the Monte Carlo analyses from Planck+BK18 datasets. We add this sentence in the abstract, introduction and conclusion. 

Please reconsider our paper for publication in Universe.

Yours sincerely,

Jun Li

Author Response File: Author Response.pdf