Effective Field Theory of Loop Quantum Cosmology

Round  1

Reviewer 1 Report

Report on: Effective field theory of loop quantum cosmology

The paper discussed the V_0 dependence of quantum cosmological models and links them to the question of infrared renormalization. The topic is interesting, timely, and doesn’t get the deserved attention in the literature. In general, the paper is well written and brings its message across. 

I have one major comment from which the manuscript would benefit:

There are two scenarios where considering the limit V_0 -> 0 is relevant

1) As the author points out, evolution of e.g. gravitational collapse may result in inhomogeneous spacetimes, whereas the initial conditions were approximately homogeneous. I would assume that most people would agree that this would require decreasing V_0.

2) Even if the spacetime is sufficiently homogeneous, one can still consider going to lower V_0, patching together the results from different patches, and comparing the result to larger V_0. This is related to the old question of few large vs many small quantum numbers in LQG, a much debated question. In this light, the author should consider the results of https://arxiv.org/abs/1811.02792, where an explicit example is given within an LQC type model that the V_0 dependence completely drops out once the individual small systems are patched together. This observation, while so far restricted to that model and the coherent states used therein, has to weaken some of the claims of the author that suggest that such behavior should not occur. In particular, I would suggest to revise the formulations in lines 31, 114, 136

Otherwise, the author may consider to cite https://arxiv.org/abs/0912.3011 in line 150, as it provides an interesting example of what may go wrong when (17) is changed within the bounds allowed by the mathematical structure of LQC. Also, it may be worth mentioning that the field \phi has density weight 1 in (29) to avoid confusion. There seems to be a “model” too much before equation (1) and another typo in line 201.

As another remark, I found the original arXiv title of the paper under consideration, “The BKL scenario, infrared renormalization, and quantum cosmology”, more descriptive. If the author wishes, he may change it back. The new title is somewhat too general. 

Concluding, I find this to be an interesting addition to the literature that deserved to be published after the author has addressed the above suggestions. 

Author Response

Thank you for these suggestions. I have inserted a brief discussion of coarse-graining in the last paragraph of section 2. However, I would like to defend my previous statements about the V_0-dependence of quantum corrections. Although the coarse-graining independence of the coherent state constructed in [32] (new reference) is interesting, I do not think that it leads to quantum corrections independent of V_0 (or the parameter j that replaces V_0 in [32]). The paper contains an explicit example (line 162) in which the classical scaling behavior is broken by quantum corrections, using the moments computed in [32].

Reviewer 2 Report

The article is very well written, with very interesting conclusions and important ones. With regard to the analysis of the renomalization in the infrared, it would be very interesting to compare the results of this article with those made in the work Class.Quant.Grav.27: 135014,2010 where the infrared (IR) effects of Lorentz violating terms using functional renormalization group methods are investigated. I believe that if a comment is added in this sense, the quality of the article will be increased. Regarding the change of signature to the Planck scale, this result not only helps the no-boundary proposal, but also many models of non-commutativity at the Planck scale as in Phys. Rev. Lett. 114 (2015) 9, 091302. Where the analysis requires a Euclidean signature.

Author Response

These are two interesting suggestions, thank you. I have inserted two statements about infrared properties in Lorentz-violating theories: One in the first paragraph of section 3, and one a few lines below equation (35). Non-commutative geometry in general and the second paper suggested by the referee are now mentioned at the bottom of page 10 (line 298).

Reviewer 3 Report

This article is a nice review of some of the recent progress in one approach to quantum cosmology. The arguments are clear and the paper is well-written. I am therefore happy to recommend this article for publication.

I do have a few questions (and caught some typos) that the author may choose to address.

The author argues for an EFT approach in quantum gravity. In general EFTs are have one important problem that does not get addressed enough: even though certain parameters are small enough to make the theory well-defined up to some energy scale, there may exist many solutions with energy cascades. This would render the predictivity of the theory much smaller than one would argue based on the running of the coupling constants. (For example, relativistic hydrodynamics is plagued with this problem.) This is clearly a question beyond the scope of this article, but I am interested to hear whether the author has any insights/thoughts about these general issues.

Some minor questions/remarks:

Adding some canonical references for the claim in line 118-121 may be beneficial to students.

Eq. (15) and (16) describe the modified Friedmann equation with quantum back-reaction included. It is not entirely clear from the description here what the limitations of this derivation are.

C is described as a correlation parameter in l.129. What does this mean? (What are typical values of this? When is it large and when is it small (what needs to be correlated)?)

In the paragraph below line 147, it says that is its clear from Eq.(12) that it cannot come from a higher-curvature model of gravity as there are no higher-derivative corrections to this equation. This statement is not entirely true; there are examples of higher-curvature models of gravity  that have second order differential equations of motion (such as Lovelock gravity, some types of f(R) gravity, etc.).

Below L. 217, it talks about replacing $K^2$. What is $K$ in this context?

In L.277, it is said that the volume of the unit 3-sphere can be used. This is not entirely clear. Why can one appeal to the unit 3-sphere and not argue for 10^x * unit 3-sphere (where x is any arbitrary real number).

A few minor typos:

Sentence below l.83 says “.....a model minisuperspace model…”.

L.95: inhomoegenetity → inhomogeneity

L.158: “The is issue” → “This issue” or “The issue”

L.190: spacial → spatial

L. 201: “therefore the” → “therefore be the”

Author Response

The possibility of energy cascades in quantum cosmology is indeed interesting. I have inserted a few sentences in the last paragraph of section 4. Thank you also for the further suggestions. The new references [25,26] indicate reviews of effective higher-curvature actions in gravitational systems. The paragraph after equation (6) now contains a more detailed explanation of the correlation parameter C and of the range of validity of this equation. In order to account for the fact that higher-derivative terms can often be rewritten as couplings to auxiliary fields (as in f(R)-theories), I have now written "higher-derivative corrections (or auxiliary fields)" when I argue that (12) does not take into account higher-curvature corrections (second paragraph of section 3). I did not specifically refer to Lovelock gravity as a counterexample because it gives rise to non-trivial modifications only in higher dimensions. I have rewritten the discussion around equations (34) and (35) in order to introduce K more carefully. Finally, the specific value of V_0 in the no-boundary proposal is not essential, but I should have emphasized that, whatever its value, it should be held constant and is not subject to infrared renormalization. The volume of the unit sphere is just one (convenient) example. This change has been made, as well as corrections of typos.