Quantized p-Form Gauge Field in D-Dimensional de Sitter Spacetime

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The authors utilized the dynamic invariant method to obtain a solution for the time-dependent Schrodinger equation and discussed the quantization of the p-form gauge field in the de Sitter Space-time. The topic and results of this paper are interesting and would be helpful to the community. The paper is technically sound and written. Hence, I think I can recommend it to be published on Universe in its current form. 

A typo: commas are missed in the equations below Eq. (14), and in Eq. (15) and (16).

 

 

Author Response

Dear referee, thank you for the report. We have fixed the typos. 

 

best regards

Reviewer 2 Report

Comments and Suggestions for Authors

The aim of authors of this manuscript is to study quantum field theory of p-form fields in de Sitter spacetime.

There is a well known and established procedure for perturbative quantization of any field in the framework of Quantum Field Theory (QFT) in both flat and curved spacetimes, see for instance Birrell & Davis 1983 book: "QFT in curved space". Indeed, authors mention this fact in the manuscript, in both introduction and conclusions. But, they do not provide any rational for their method. On the other hand, their work and method have many problems that I explain in more details below. For these reasons, I cannot recommend publication of this manuscript in present form.

Main issues
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- The authors claim quantization of p-form fields. But, there is no explicit expression for the p-form field A_i1...ip defined in the paragraph after equation (2).

- There is a confusion between quantization and solving field equation (or mode equation) (3), which is also relevant for classical fields.

- The authors claim to have discovered a similarity between the field equation of the p-form field in a time dependent flat background geometry and Schrodinger equation for an oscillator. This is not a surprise, because the origin of the wave-like field equation is the wave-like Schrodinger equation. This work does not add anything to established knowledge.

- The work proceeds by defining a constant of motion I for the mass-varying oscillator, which lacks any physical interpretation. They define a pair of creation and annihilation operator for eigen states of I. But, no connection is established with the p-form field.

- Finally, a solution is obtained for the mode equation (5) in a de Sitter background. However, this equation could be solved from the beginning and without passing through the analogy explained above. Moreover, from equation (26) it is clear that for the general form of the solution is independent of the value of p. In particular, in the
case of p = 0 and p = 1 - a scalar and a vector, respectively - which are widely used in inflation models, these solutions are well known in the literature and their extension to p-forms for the decomposition (4) is trivial. Therefore, the present work does not provide any new insight, except for diversion and confusion.

Other comments
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In the decomposition (4) the authors do not explain what is the motivation for separation of r1 and r2 from polarization f_i1....ip and how it is done.

Comments on the Quality of English Language

The English is fine and needs only minor revision.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf