Non-Commutative Classical and Quantum Fractionary Cosmology: FRW Case

Round 1

Reviewer 1 Report

This manuscript studies the noncommutativity effect to the FRW cosmology with K-essence dark energy. By introducing the noncommutative variables, the authors get the modified symplectic structures of the system. The authors also find that the separation of variables are different from previous literatures. And they finally result in the complex fractional differential equations. The interesting thing is that the authors find that the probability density undergoes a shift back to the direction of the scale factor, causing the classical evolution to arise earlier than in the commutative world. This is due to the noncommutative effect. 

I found that this paper can contribute to the field of noncommutativity and the results sound good. The paper was well written and the grammars were fine. Therefore, I suggest to accept this manuscript. 

Author Response

see the attached file

Author Response File: Author Response.pdf

Reviewer 2 Report

In this paper, the authors explore the effects of non-commutativity in fractional classical and quantum schemes using the flat  (FRW) cosmological model coupled to a scalar field in the K-essence formalism.

The manuscript is written enough and the calculation seems correct. The results presented in this manuscript are worth publishing.  Furthermore, this manuscript could be improved if the authors added some illustrations about the observational effect of the presenting result. 

Author Response

see the attached file

Author Response File: Author Response.pdf

Reviewer 3 Report

The paper appears reasonable. However, some comments arose about it. I enumerate them below. Before a fully-acceptance, I would ask the authors to refine the manuscript accordingly.

First, I don't understand the physics related to the real and imaginary part of the findings made by the authors. I would ask more explanations about that. For example, once we consider a scalar field with imaginary part, we could associated it with charge. But here?

Second, the authors might carefully emphasise the differences that occur between their work and the standard model. Which kind of significant departures could be expected, even in view of current experimental developments? Why should we prefer this approach to the standard one?

Third, fractional calculus usually induces non-locality. In the case of the authors, how non-locality is physically interpreted?

Fourth, in connection with point no. 3 above, I would need that the authors clarify why the universe age appears bigger. However they made some comments in the text, they are contradicting the standard model expectations. So, physically speaking, how do the authors justify their outcome?

Five, the role of K-essence is not clear to me. Where the presence of modified kinetic term exactly enters their approach? For example, in 2309.03065,2204.02190 it is possible to reinterpret the role of a different kinetic term throughout the slow roll regime. Can the authors explain which role is here expected? And, why they're considering a K-essence model? 

Moreover, the paper can be improved in style and English before resubmission.

I like the overall manuscript and the idea is intriguing. I would prefer to see the manuscript again, in any cases. 

Just moderate changes could be useful about English and style.

Author Response

see the attached file

Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

The paper has been adequately improved. I think it is now suitable for being accepted for publication.

English may require a minor improvement. I think the proof-reading process by the journal would be enough for that.