Perturbations in Bianchi-V Spacetimes with Varying Λ, G and Viscous Fluids

Round 1

Reviewer 1 Report

This paper “Perturbations in Bianchi-V spacetimes with varying Lambda, G and viscous fluids” by Abebe et al. deals with how cosmological perturbations evolve in the Bianchi type-V anisotropic universe. In the model, the cosmological constant and the gravitational constant change with time, and the presence of viscosity is additionally considered. The key point of this paper is that, compared to the evolution of matter density perturbations in the SCDM(\Omega_m=1) and LCDM models, the evolution of density perturbation evolves more rapidly in the Bianchi type-V model, and if viscosity is further added, the structure formation becomes more active. This paper is interesting because it contains new information on the evolution of perturbation in the Bianchi-V model with viscous fluid. However, there are some issues that readers may raise in common about the results, and I suggest that sufficient explanations for these issues should be added in the revised version. It would be nice if the authors provided an explanation for the points I have listed below.

 

1. Figure 2 shows how \Omega_\Lambda changes with redshift z, which appears to be consistent with the standard LCDM model. However, according to the authors' previous paper, the evolution of matter density parameter \Omega_m shows a very different behavior from the LCDM model. I suggest that the authors provide an appropriate explanation as to why \Omega_m shows this kind of behavior. Besides, I suggest that the authors display \Omega_Lambda, \Omega_matter, \Omega_sigma, and \Omega_\chi together in Figure 2 by increasing the redshift range from the very early epoch to the present epoch (with a logarithmic scale) in order to clearly show how these components change with time. It will be even better if the radiation component is added here. This is necessary for us to understand the overall evolution of the background universe in this model. 

 

2. The  1+3 covariant formalism was used to describe the perturbed quantities in the Bianchi-V model. Since many researchers follow the method based on the metric formalism, I suggest that the authors explain in more detail what advantages are expected in the covariant formalism compared to the metric formalism.

 

3. As for results of the evolution of matter density perturbations, the authors presented only those for specific alpha=0.312, beta=1, n=0.2 values ​​(line 116), but it is necessary for the authors to show how the results change for varying viscosity parameters. 

 

4. Although the text describes that the amplitude of the matter density perturbation in the Bianchi-V model without viscosity is larger than those of pure GR and LCDM models (line 121), Figures 3 and 4 do not show such a trend.

 

5. In Figures 5 and 6, it is seen that the long-wavelength perturbations grow much more than the short-wavelength ones, and the last sentence of this paper also mentions this result. It is worth mentioning explicitly that models giving such an infrared divergence are not observationally acceptable. In addition, in Figure 6, the perturbation of short wavelengths increased over time, and then the amplitude decreased near the present epoch. It is difficult to understand the phenomenon in which the density fluctuations decrease during the formation of cosmic structures. Thus, a proper discussion is needed to justify this phenomenon, and it is also necessary to explain why such a phenomenon did not occur in long wavelengths.

Author Response

Reviewer, Thank you so much for your time.

The letter of response is enclosed.

Thanks 

Author Response File: Author Response.pdf

Reviewer 2 Report

The paper presents drawbacks that I can't understand at all. I invite the authors to carefully revise the manuscript according to the following requests.

First, who guarantees that the deceleration parameter in eq 16 is under that form? In spacetime different from FRW I expect that its form cannot be the same as in FRW. There's a wide literature about this. It seems that the authors are making an assumptions and I don't undestand physically how to support it.

As a consequence of the above, I don't understand eq. 30; is it correct? From it all perturbations follow but, again, the structure is analogous to FRW, albeit we're not in a homogeneous and isotropic case.

Second, why the authors chose Bianchi V and not others? Which differences may occur with Bianchi I and IX? The latter is one of the most likely ones, so which departures can be expected?

Two minor points, that however deserves careful revisions, are also raised.

A) The authors cite "pure GR" to indicate Omega_m=1 and Omega_L=0. First, in a universe with Lambda, there is no need of going further FRW, as it is well-known from observations. So the Bianchi case would be useless. Hence, why including Lambda? Explanations! But moreover, pure GR is misleading! GR is a theory that requires a metric to get dynamical equations and the cosmological constant is a solution of the equations themselves. Set it to zero and claim "pure GR" is meaningless! The authors should revise it, since we're not working on extended theories of gravity in which there's the need to specify "pure GR" VS alternative gravities.

B) The variation of fundamental constants appears here to me as a mere exercise and physically not clear to me. Why should we care in this paper, physically speaking?

C) English and style look poor. A revision of the whole is required.

After these change I want to see the manuscript again. But I invite the authors to carefully revise it because under present form I am not satisfied about the overall quality.

Author Response

Reviewer, Thank you so much for your time.

The letter of response is enclosed.

Thanks 

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The authors have revised the manuscript to clarify the points raised in the previous report by adding appropriate sentences and figures. Although the evolution of density fluctuations presented in this paper may not provide observationally consistent results, I think that this paper is interesting because it contains new information about the evolution of perturbations in the Bianchi-V model with viscous fluids. Therefore, I recommend that this paper be published in Universe.

There are places where the newly added sentences or expressions are not smooth. Please make sure there are no errors (e.g., sentences on lines 182-190; n=0,2 in captions of Figs. 8 & 9). 

Author Response

Dear Reviewers,
We have made minor revisions to the manuscript, incorporating some of the typographical corrections suggested.
The comments on the issues raised by the referees are in the attachments:

Author Response File: Author Response.pdf

Reviewer 2 Report

The paper is sufficiently improved. It can be now accepted

Author Response

Dear Reviewers,
We have made minor revisions to the manuscript, incorporating some of the typographical corrections suggested.
The comments on the issues raised by the referees are listed in the attachment below:

Thanks

Author Response File: Author Response.pdf