Review Reports

Round 1

Reviewer 1 Report

I have found this paper of interest. I mean it not just from a personal (my own) scientific line of research but also because it opens new ground on a broader scope, towards more groups and research topics, where the ideas can be employed. I think it produces a welcome approach, a constructive, positive contribution.  

 

The paper is sound and innovative in contrasting three approaches and could mention a few more. I think the authors would benefit from considering, even if briefly alluring, like with one or two more  gentle strokes, as in an elegant landscape painting, if mentioning the issue of time retrieval through perturbations and canonically in 

 

A. loop quantum gravity 

a1. arXiv:1802.02382

Space and Time in Loop Quantum Gravity

Carlo Rovelli

 

a2. C. Rovelli, “Statistical mechanics of gravity and the

thermodynamical origin of time,” Class. Quant. Grav.

10 (1993) 1549–1566.

 

 a3. G. Chirco, T. Josset, and C. Rovelli, “Statistical

mechanics of reparametrization-invariant systems. It

takes three to tango.,” Classical and Quantum Gravity

33 (2016) no. 4, , arXiv:1503.087

 

B. supersymmetric quantum cosmology:

 

b1. gr-qc arXiv:gr-qc/9603054

Cosmological Time in Quantum Supergravity

 

Robert Graham, Hugh Luckock

 

b2. Origin of structure in supersymmetric quantum cosmology

Vargas Moniz, P.

Physical Review D - Particles, Fields, Gravitation and Cosmology, 1998, 57(12), pp. R7071–R7074

 

b3. Quantum cosmology - The supersymmetric perspective - Vol. 2: Advanced topics

Moniz, P.V.

Lecture Notes in Physics, 2010, 804, pp. 1–297 (see chapters 2, 4 and 10)

 

b4. Semiclassical approximation to supersymmetric quantum gravity

Kiefer, C., 

Lück, T., 

Moniz, P.

 

Physical Review D - Particles, Fields, Gravitation and Cosmology, 2005, 72(4), pp. 1–19, 045006

 

 

C. String quantum cosmology.

c1. Quantum String Cosmology

by Maurizio Gasperini 

 

Universe 2021, 7(1), 14; https://doi.org/10.3390/universe7010014

c2.Gasperini, M.; Maharana, J.; Veneziano, G. Graceful exit in quantum string cosmology. Nuc. Phys. 1996, 472, 349. 

 

c3. Gasperini, M.; Veneziano, G. Birth of the universe as quantum scattering in string cosmology. Gen. Rel. Grav. 1996, 28, 1301.

c4.  Lidsey, J.E. Bianchi-IX Quantum Cosmology of the Heterotic String. Phys. Rev. 1994, 49, R599.

1. c5. Lidsey, J.E. String quantum cosmology of the Bianchi class A. arXiv 1994, arXiv:gr-qc/9404050. 

 

 

So, this paper is worthy, and I can recommend it for publication. It is correct, a mentionable review and worthy exercise of analysis and synthesis, pointing to new directions of research, contrasting and establishing points of correspondence among apparently different approaches. The authors may consider the above list as mere suggestions to enrich (in my opinion) their review paper and reach the interest of a much broader audience if doing as such. A wider and broader review and earnest display of routes (within the scope of the subject discussed - the emergence of time in quantum gravity approaches) is of merit and the more cases pointed, the better for readers, journal readership and surely the authors' recognition by the community). On the whole, I do recommend this paper.

Author Response

Dear Reviewer,

Thank you for your comments. We have taken them into account and added a number of references on works where the problem of time is discussed, including those recommended by you.

Thus, we added the references [17-33] and the following paragraph into Introduction (page 2, lines 71-80):

In fact, one can hardly name a physicist who would deal with quantum gravity and would not write about the problem of time. In the framework of the Wheeler – DeWitt quantum geometrodynamics, let us mention the well-known and often cited review papers by Kuchař [17] and Isham [18]. Among the others are the papers [19,20] and the recent work [21]. In the framework of supersymmetric quantum cosmology, we would like to refer to the paper [22,23] and, especially, to [24,25], where the semiclassical approximation is also discussed. Some aspects of the problem of time are touched in string cosmology [26–30]. The relation of the problem of time with statistical mechanics is analysed in [31,32]. The apologists of loop quantum gravity insist that the very notions of space and time must be modified [33]. This list can be continued…

On behalf of R. I. Ayala Oña and D. P. Kislyakova,
Yours sincerely,
Tatyana Shestakova.

 

Reviewer 2 Report

The authors study the problem of time in quantum gravity (QG). Time is absolute in  quantum theory whereas it is dynamical in general relativity. The combination of both theories into a theory of QG  leads therefore to a "problem of time". This is also evident at the level of the Wheeler – DeWitt equation in quantum geometrodynamics. There is no time derivative  in it. The authors analyze these problems. In particular, they  study the semiclassical limit in the case of a closed isotropic model with  a scalar field decomposed into modes and consider the  calculations made within frameworks of three approaches.  In the approach by Kiefer and collaborators, there was no time in the Very Early Universe,  which is  the realm of QG, and contend that time  appeared only at the semiclassical stage when the description could eventually be made from the point of view of quantized fields in a classical geometric background.  The systematics in the presentation by the present authors is to first study the equations for a wave function of the Universe in the  extended phase space approach and the Wheeler – DeWitt geometrodynamics.  Next they consider the semiclassical limit and the highest orders of expansion in a power series of the inverse of a large mass parameter M.  Finally they use various approaches to obtain a temporal Schrödinger equation for matter fields with a background  gravitational field, where there is no time problem. In the end the problem of time in QG returns any analysis to the question, what equation is  more fundamental, the Wheeler – DeWitt equation or the Schrödinger equation. The answer to this question is not given since at the moment cannot be known. But the discussion is sufficient and I have no objection to the publication of this paper in its present form.

Author Response

Dear Reviewer,

Thank you for your comments and your positive assessment of our work.

Following the recommendations of Reviewer #1, we have added new references [17-33] on papers where the problem of time is discussing.

On behalf of R. I. Ayala Oña and D. P. Kislyakova,
Yours sincerely,
Tatyana Shestakova.