An Analytical Approach to the Universal Wave Function and Its Gravitational Effect
Round 1
Reviewer 1 Report
The paper should be revised according suggestions contained in the enclosed pdf file.
Comments for author File: 
Comments.pdf
Author Response
Response to Reviewer 1 Comments
Point 1: The Hamiltonian appearing in Eq. (1) is not described.
Response 1: We have given a brief description of based on this suggestion.
Point 2: Also there is a problem with the choice of the initial form Ψu(t0) of Ψu(t), which should be explained in more precisely. In this context it may be interesting for readers of the paper to know what is a relation between the initial value of Ψu(t) and the initial wave function of the Universe (se e.g. [1])?
Response 2: See lines 286-289 in page 12.
Point 3: What is a relation of Ψu(t) with the wave function of the universe (see e.g. [2])? Is there any connection of Ψu(t) with the Feynman path integrals (see e.g. [3])? Is there any connection between Ψu(t) and solutions of the Wheeler – DeWitt equation? .
Response 3: See lines 289-298 in page 12.
Point 4: What is the relation of ideas presented in the paper with the the discussion of the Everett’s universal wave function presented in other papers?
Response 4:.See lines 408-410 in page 15.
Reviewer 2 Report
The authors work out an analytical approach to the universal wave function and analyze, in particular, its gravitational effect. Thus, they deal with a quite fundamental problem, which was originally introduced by Everett. However, the whole manuscript is written not quite clearly. It becomes not transparent what are the concrete assumptions and what are the derived conclusions. The authors claim to have shown that the universal wave function can have observable gravitational effects – but I can not follow the concrete derivation. Therefore, the main idea of the manuscript should be presented in a more transparent way before it could be reconsidered for publication.
Author Response
Point 1: Therefore, the main idea of the manuscript should be presented in a more transparent way before it could be reconsidered for publication.
.
Response 1: We have revised significantly the manuscript. (i) We have reorganized the manuscript by including the content of the appendix of the previous version to the main body, in order to make it more coherent to read the paper. (ii) In page 3 and page 4, we added an introduction to the key idea of our work in lines 90-124.
Please check in the attachment.
Thank you.
Author Response File: Author Response.pdf
Reviewer 3 Report
This is an incredibly bold paper. The problem I have with it, is due to the extension of the wavefunction of the universe idea, and Dark Matter
So being the case I have attached the one and only one arXIV article which may have , in motivation, some of the same thinking, and that paper I am including is a so called "A Quantum origin to Dark matter" which does not involve exotic particles
I would urge the people responsible for the paper I am reading and judging to go over the attached PDF file and to comment on it.
The other issue is that I am awaiting is experimentally falsifiable predictions from the presented work
If both are done, I will then approve the paper
Aside from that, this is nothing like I have ever seen before. and is novel enough to warrant publication
Comments for author File: Comments.pdf
Author Response
Point 1: I would urge the people responsible for the paper I am reading and judging to go over the attached PDF file and to comment on it.
Response 1: See lines 472-478 in page 16.
"Note added: After the submission of our manuscript, the referee noticed a relevant paper [18] which argues that the solution of the Schrödinger equation including the gravitational potential may provide the possibility to explain the dark matter. However, the mechanism to explain the dark matter is completely different from our manuscript. In [18], the single-particle Schrödinger equation is used to explain the dark matter gravitational effect; while in our work the diffusion wave packet for themany-body universewave function is shown to explain the gravitational effect of dark matter."
[18] A. D. Ernest, A quantum approach to dark matter, arXiv: astro-ph/0406139 (2004).
Point 2: The other issue is that I am awaiting is experimentally falsifiable predictions from the presented work.
Response 2: See lines 420-471 in page 15 and page 16.
Please check in the attachment.
Thank you.
Author Response File: Author Response.pdf
Round 2
Reviewer 3 Report
I accept the document as being worthy of being published in Symmetry
