Thermal Effects in Ising Cosmology

Round 1

Reviewer 1 Report

This paper considers a real scalar in 4D de Sitter (dS) spacetime. The author continued developing their previous proposal in ref.[14], where they argued that the cosmological spectral index may be controlled by the critical exponent in the boundary 3D Ising model, in the context of dS/CFT. While ref.[14] focused on the boundary field theory, the current paper develops the bulk construction in dS and attempts to use the critical exponent in 3D Ising model to fix various cosmological observables.

The central idea of the paper sounds appealing, disregarding its concreteness. In particular, there is evidence that the CFT dual of dS has to be non-unitary. However, the Ising model is unitary. It might be that the observables are sufficiently universal such that the correspondence to the critical exponent in the Ising model still works? I cannot find any clear justification through the paper arguing for the validity of using the Ising model as a CFT dual of dS spacetime. There seems to be some argument along these lines in ref.[14], but I cannot say that I fully understand.

The introduction of the paper is rather brief. It would be very useful if the authors could comment on the background of this study and give some qualitative arguments for why the idea of "Ising cosmology" could work. Moreover, it would be helpful if the authors could preview clearly what new results are in this paper. 

The abstract of the paper indicates that the computation of the thermal propagators of the real scalar in dS spacetime is part of the new results in this paper. Judging from page 5, it seems that the contribution of the paper is limited to that it shows the dS thermal propagator in ref.[9] "can be equivalently obtained via a TFD rotation of the zero temperature Schwinger-Keldysh propagator." This is what one would expect. However, how the formalism developed in this section is useful in any direct way for the later applications to the spectral index with thermal effects is not very clear to me. 

Near the end of the paper, the authors presented the central results in eqs.(3.9), (4.3) and (4.6), predicting the values of various cosmological observables. It is then claimed in the conclusions that these values are "well within current experimental bounds." It would be useful if the authors could actually present the comparisons to the experimental bounds explicitly in this paper.

I cannot recommend the paper for its publication in the journal unless the above issues can be addressed.

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I also collected a series of more technical remarks below:

Sec.2 is mostly clear to me, except a few minor points:

(1) On page 2, "Bunch-Davies" should be "Bunch-Davies (BD)", as the abbreviation "BD" shows up on page 4.

(2) The Kadanoff-Baym-Keldysh-Schwinger contour on page 3 should not be closed one its left end. It could be useful to add in the labels C_-, C_+ and C_3 for different segments of the contour.

(3) eq.(2.16) seems to have a typo, where the numerator of the second term on the left hand side should be e^{-β ω_|k| / 2} instead of 1.

In sec.3, the interesting-looking eq.(3.2) does not have any derivation or reference. In eq.(3.7), the quantity P_{S,β}, which seems to be the power spectrum, is introduced without any explanation. Moreover, below eq. (3.9), I am confused about what the equation Γ_θ = η - η really means.

In sec.4, I am not sure about what "a line of constant physics" means. It would be nice if a precise definition of this terminology could be given. 

Author Response

Please find attached our response to the comments of Referee 1.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments for author File: Comments.pdf

Author Response

Please find attached our response to the comments of Referee 2.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The authors have carefully addressed the previously raised issues and have included further edits of the text. I have read through all the new edits and they look reasonable to me. I think the presentation of the paper has been significantly improved, which makes their results clearer and more convincing. Therefore, I recommend its publication in the journal Universe.  

Reviewer 2 Report

The problem of Hermitian de Sitter Hamiltonian is a delicate subject and needs more consideration.