Study of Nonlinear Evolution of Spacetime Fluctuations in Quantum Gravity Inflation for Deriving Primordial Spectrum

Round 1

Reviewer 1 Report

Dear authors

I have read your manuscript with interest.

I have the only essential comment. The inflationary paradigm was first suggested by Gliner. E.g see Refs in

https://doi.org/10.3390/universe9010046

Author Response

Thank you for carefully reading the manuscript. I have added footnote 1 and reference 4 following your suggestion. Additionally, I added footnote 10 and reference 45 in response to a suggestion from another reviewer.

Reviewer 2 Report

The author studies evolution of quantum fluctuations of gravity around an inflationary solution in renormalizable quantum gravity. Inflation ignites at the Planck scale and continues until spacetime phase transition occurs. The author shows that during inflation, the initially large scale-invariant fluctuations reduce in amplitude to the appropriate magnitude suggested by tiny CMB anisotropies. This research derived spectra of scalar fluctuations at the phase transition point.  In this paper, the author determines and examines various nonlinear terms, not treated in previous studies. These result can lead to a derivation of the precise primordial spectra and, could, in the future lead to the resolution of the problem of cosmology tensions. The paper is well structured and well written, no issues detected. The paper can be published in the current form.

Author Response

Thank you for carefully reading the manuscript. I added footnote 1 and reference 4, as well as footnote 10 and reference 45, in response to suggestions from other reviewers.

Reviewer 3 Report

This paper extends previous work by the author and others, based on the assumption that quantum gravity can be described by the renormalizable four-derivative theory. In this picture the theory is asymptotically free in the trans-Planckian regime and the Planck scale is obtained by dimensional transmutation, in a similar fashion as the QCD scale. Einstein gravity is obtained as an effective low energy theory.

This paper is devoted to a derivation of the primordial spectrum of fluctuations from these first principles. Even though this requires several approximations and numerical evaluation, the results are interesting and promising.

I recommend this paper for publication in Universe.

x

Author Response

Thank you for carefully reading the manuscript. I added footnote 1 and reference 4, as well as footnote 10 and reference 45, in response to suggestions from other reviewers.

Reviewer 4 Report

This is very well-written paper and on a very interested subject. The article deals with the effects of quantum cosmology in the early stages of the universe. The results are correct and of special importancy. The study fits on the scopus of the journal and I am happy to recommend it for publication. 

Nevertheless, I want to ask the author to revise his work by introducing a discussion on another attempt of quantum cosmology, based on the Bohmian representation and include a discussion between the two different approaches. 

Author Response

Thank you for carefully reading the manuscript. I have added footnote 10 and reference 45 following your suggestion. Additionally, I added footnote 1 and reference 4 in response to a suggestion from another reviewer. 

In the footnote 10, I have only mentioned matters that seem to be relevant in terms of the interpretations. This is because, as far as I know, Bohmian cosmology is based on Einstein gravity composed of second derivatives, so it is difficult to make a comparative study since the setting and the quantization method are different from my approach. Since this is a research paper, not a review, it is not appropriate to discuss such a specific model in detail. On the other hand, the interpretation seems to be a common issue regardless of the gravity models. I have cited a well-written review on this topic as a reference, in which cosmological issues similar to those discussed in my paper are addressed using the modified Wheeler-DeWit equation involving quantum potential.