Probing the Dark Universe with Gravitational Waves

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper discusses the propagation of linear metric perturbations including their possibile interaction with cosmic matter sources. The presented results can be generalized to higher orders, and may have phenomenological  applications concerning tests of the GW effective speed and polarizations. I recommend publication.

As an optional improvement the author could explicitly note that the non-vacuum propagation equation (34), used in this paper, agrees with the more general non-vacuum GW equation already derived in JCAP 07 (2021) 021, once one imposes the so-called trasversality (or Lorentz gauge) condition of Eq. (28).

Author Response

I thank the Referee for the comments and suggestions. I give below my replies.

The paper discusses the propagation of linear metric perturbations including their possibile interaction with cosmic matter sources. The presented results can be generalized to higher orders, and may have phenomenological  applications concerning tests of the GW effective speed and polarizations. I recommend publication.

As an optional improvement the author could explicitly note that the non-vacuum propagation equation (34), used in this paper, agrees with the more general non-vacuum GW equation already derived in JCAP 07 (2021) 021, once one imposes the so-called trasversality (or Lorentz gauge) condition of Eq. (28).

REPLY

The suggested references to the equation without gage fixing have been added.

 

Reviewer 2 Report

Comments and Suggestions for Authors

In the paper under review,  the author presents a gauge invariant effective equation derived under the proposal of having an interaction of gravitational waves with other fields or by considering the effects of gravity modification. The author shows that it is possible to have an equation which is not only gauge invariant but with perturbations invariant under time conformal transformations. 

Under these assumptions it is shown that direct effects could be observed and measured concerning the propagation time delay and the luminosity distance ratio between gravity and electromagnetism waves. This could imply the possibility to measure the interaction of gravitational waves with dark energy or dark fields, among other interesting consequences.

I consider this article well written and interesting, for which I recommend its publication in its present way. I just would like to suggest some possible minor changes which could improve the manuscript:

1.  In Eq. (33) the notation used is not common (at least to me). Could you explain the meaning of those little symbols?

2. In line 161, the author mentions the TT gauge, but I didn´t find what TT stands for.

3. A careful review of the complete text in order to find other possible terms which have not been properly defined.

 

 

Author Response

I thank the Referee for the comments and suggestions. Replies can be found below.

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In the paper under review,  the author presents a gauge invariant effective equation derived under the proposal of having an interaction of gravitational waves with other fields or by considering the effects of gravity modification. The author shows that it is possible to have an equation which is not only gauge invariant but with perturbations invariant under time conformal transformations. 

Under these assumptions it is shown that direct effects could be observed and measured concerning the propagation time delay and the luminosity distance ratio between gravity and electromagnetism waves. This could imply the possibility to measure the interaction of gravitational waves with dark energy or dark fields, among other interesting consequences.

I consider this article well written and interesting, for which I recommend its publication in its present way. I just would like to suggest some possible minor changes which could improve the manuscript:

1.  In Eq. (33) the notation used is not common (at least to me). Could you explain the meaning of those little symbols?

REPLY

Below eq.(33) it has been added the explanation that E denotes the Einstein frame. 

     2. In line 161, the author mentions the TT gauge, but I didn´t find what TT stands for.

REPLY

At the beginning of that paragraph it has been added what TT stands for (transverse traceless).

     3.  A careful review of the complete text in order to find other possible terms which have not been properly defined.

REPLY

The text has been reviewed to make sure all terms are properly defined.