Quantum Effects on Cosmic Scales as an Alternative to Dark Matter and Dark Energy

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Summary:

The authors propose an extension of the spin-torsion theory, which integrates the quantum spin of macroscopic matter on cosmic scales. By incorporating the Dirac equation and substituting the constant mass with a scale function, the authors introduce a quantum potential energy (QPE) term that scales with gravitational systems. This QPE term induces time dilation and distance contraction, mimicking the effects traditionally attributed to dark matter and dark energy. The theory is rigorously tested against cosmological data, specifically the luminosity distance-redshift relation of Type Ia Supernovae (SNe Ia) and galaxy rotation curves from the SPARC database, demonstrating a robust alignment with observations.

There are several limitations to be addressed:

1. The authors assume that the Dirac spinor and Dirac equation can fully capture the essential physical characteristics of macroscopic particles. Justification shall be made. Will the assumption lead to a violation of the de Broglie hypothesis? Some discussion needs to be added to convince the audience about the quantum property of macroscopic particles. 

2. The functional form of the scale-dependent parameter \alpha(\lambda), which determines the strength of the QPE, is not derived from first principles and must be determined through observations, limiting the theory's predictive power.

3. The derivation of section II leads to the inclusion of quantum effects (QPE) in the mass term. How is this related to or different from the torsion field in Einstein-Cartan Gravity? When deriving the QPE, the author utilizes the Einstein equation, i.e., adopts the physical theory behind the Einstein equation. The author needs to discuss whether the proposed new theory will lead to modifying Einstein's equation in the first place. If not, explain the applicability or compatibility of the Einstein equation and the proposed theory. 

4. The theory’s applicability may need extended to be more convincing. 

For the galaxy, how could the theory explain the bullet cluster, which is considered the best evidence for the existence of dark matter?

In cosmology, how could the theory explain the cosmic microwave background? If a static university was yielded in the model, a section on the model’s implications for cosmic evolution may be desired. 

While the innovative approach and rigorous mathematical framework are commendable, the theory's assumptions and empirical dependencies need addressing. Revising the paper to tackle these weaknesses would significantly strengthen its contributions to the field.

 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Report Ms. Universe-3126993

  The unification of quantum mechanics and general relativity is one of the central themes of contemporary physics, addressed by many authors, but pending a solution. The authors are attacking that intricate problem from a very specific viewpoint, namely to describe matter in terms of  Dirac spinors.  The approach leads to a cosmology postulating a static universe, apparently being free of dark matter (DM) and dark energy (DE). In the presented approach the effects usually attributed to DM and DE are  taken care of by a quantum potential.    On first sight, the results are intriguing. A closer inspection, however, reveals that the work suffers from a multitude of severe problems and misunderstandings:

1. Dirac theory is intimately connected to antimatter and vacuum polarization which are treated properly only by a full-fledged quantum field theory as realized e.g. in QED and QCD. The authors seem to ignore those subtleties, at least they are not addressed in the paper.
2. An important consequence of covariance and of the Clifford algebra underlying Dirac theory is the appearance of a variety of vector and axial vector currents and scalar and pseudo-scalar densities. The “density” considered by the authors, commonly known as “vector density”,  is in fact the time-like component of a vector current j_\mu. In Dirac-theory the vector current is part of the canonical four-momentum and couples to four-vector fields. It is not part of the mass. 
3. Since the vector current transforms like a four-vector the “density” considered in the paper depends on the Lorentz-frame. Obviously the authors do not take into account that important property.
4. Because of their content of negative energy components, Dirac-spinors  inevitably lead to  another type of densities, namely the scalar densities. They are Lorentz-invariant, couple to scalar fields and may give rise to mass terms. The paper lacks a discussion of that issue which is central to the proper treatment of an interacting Dirac theory.
5. Finally, a puzzling aspect of the approach is that quantum effects mysteriously disappear at “every-day” macroscopic scales up to the solar system, but recover on galactic and cosmic scales. That aspect is not explained in due detail. It seems that the approach is in fact a collection of three different schemes without a clear separation/definition of the separating scales.

  Apart from other questionable aspects, the multitude of deficiencies in the basics of Dirac theory alone disqualifies the paper from publication.  In its present form, the paper must be rejected.   

 

Comments on the Quality of English Language

  No comments

Author Response

please see the attachment

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

I would like to thank the authors for their thoughtful revisions and detailed responses to my previous comments. After reviewing the revised manuscript and the responses provided, I have minor points to address for further clarification and improvement of the manuscript.

1. Justification of the Dirac Spinor and Dirac Equation for Macroscopic Particles

The authors have added additional discussion to justify the assumption that the Dirac spinor and Dirac equation can fully capture the essential physical characteristics of macroscopic particles (pages 2-4). I appreciate this addition, and the discussion provides a clearer understanding of the underlying assumptions. However, while the explanation regarding the de Broglie hypothesis and its compatibility with the macroscopic quantum properties is convincing, I recommend adding a more detailed comparison with existing literature exploring similar quantum mechanics extensions to macroscopic scales. This would help position the authors' work within the broader context of ongoing research in this area.

2. Relation to Torsion Field and Modification of Einstein's Equation

The authors have addressed the question regarding the relation of their work to the torsion field in Einstein-Cartan Gravity (pages 3-4). The clarification that their work using Gauge Theory Gravity (GTG) is nearly equivalent to Einstein-Cartan Gravity and represents a modification to general relativity is a valuable addition. However, I suggest a more explicit discussion on how this equivalence influences or constrains the predictions of the new theory. Additionally, it would be beneficial to include some concrete examples or calculations demonstrating this equivalence's implications in specific scenarios.

I recommend the manuscript for publication after these final revisions are considered.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

By revision, the paper has been improved considerably, now qualifying for publication. The paper is recommended for publication.

Comments on the Quality of English Language

no comment

Author Response

Thank you very much for your comments!

Round 3

Reviewer 1 Report

Comments and Suggestions for Authors

The authors address the issues in the previous rounds well. I don't have any more comments.