Pith. sign in

REVIEW 15 references

Exact Recession Velocity and Cosmic Redshift Based on Cosmological Principle and Yang-Mills Gravity

T0 review · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Within Yang-Mills gravity, the paper derives a nonlinear recession-velocity law with an upper speed limit and identifies cosmic redshift with the special-relativistic Doppler formula evaluated at that velocity.

arxiv 1908.01585 v1 pith:XGUABVX2 submitted 2019-08-01 physics.gen-ph

Jong-Ping Hsu , Leonardo Hsu This is my paper · ORCID
classification physics.gen-ph
keywords cosmicframerecessionexactinertialpartialvelocityaccelerated
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Most cosmologists describe the expanding universe with general relativity, where distant galaxies recede from us at speeds that can, in principle, exceed the speed of light. This paper works inside a different framework, Yang-Mills gravity, which treats gravity as a flat-space gauge theory and produces an effective metric for macroscopic motion. Applying the cosmological principle, the authors take the effective metric to depend only on time, with both scale factors proportional to the square root of the cosmological clock time. For a galaxy of mass m, they write a Hamilton-Jacobi type equation, the Okubo equation. Solving it gives an exact recession velocity, dot r = rH/[1/2 + sqrt(1/4 + r^2 H^2/C_o^2)], that reduces to Hubble's law for small distances but approaches a limiting speed C_o at large distances. That limiting speed is the ratio of the two scale factors and, in their model, equals the cube root of 3 omega, where omega is the ratio of pressure to energy density of matter. The paper does not pin down omega. The same machinery is applied to light. The authors assume light obeys a massless version of the Okubo equation and then invoke a principle of limiting continuation to connect the emitted and observed wave vectors. The resulting redshift relation, z = (1+V_r)/sqrt(1-V_r^2) - 1 with V_r = dot r/C_o, is algebraically identical to the ordinary special-relativistic Doppler formula. For small velocities it reproduces the low-redshift Hubble behavior. The paper's real new content is therefore the exact velocity law and its upper limit, not the redshift formula itself.
Extended reading notes

Core claim

The central claim, stated in the abstract and Eq (20), is: 'This cosmic equation predicts an exact recession velocity, dot r = rH/[1/2 + sqrt(1/4 + r^2 H^2/C_o^2)] < C_o' with C_o = B/A = (3 omega)^{1/3}, and the exact redshift z = (1+V_r)/sqrt(1-V_r^2) - 1 with V_r = dot r/C_o. If the paper is correct, Hubble's law is the low-velocity limit of a gauge-theoretic Okubo equation and recession speeds are bounded by an effective speed of light C_o.

Load-bearing premise

The load-bearing premise is the cosmic solution G_munu(t) = diag(B^2, -A^2, -A^2, -A^2) with A = alpha t^{1/2}, B = beta t^{1/2} and C_o = B/A = (3 omega)^{1/3}, taken from the HHK model [10] and stated in Sec 2, Eq (11). If the T4 field equations do not actually yield this solution, or if a matter-dominated universe has pressure P = 0 so that omega = 0, then C_o vanishes and the exact recession velocity and redshift formulas lose meaning. The paper neither rederives this solution nor justifies the nonzero omega needed for C_o > 0.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Assumptions & free parameters 1 free parameters · 8 assumptions · 1 invented entities

The central formulas rest on the imported HHK scale-factor solution, the Okubo equation as an equation of motion, and the assumed Doppler-type transformation for light. The only genuinely free numerical parameter is omega, which controls C_o; the auxiliary frame F_e is a conceptual device rather than an observable entity.

free parameters (1)
  • omega (pressure-to-energy-density ratio), equivalently C_o = B/A = (3 omega)^{1/3}
    The upper limit C_o of the recession velocity and the final redshift prediction depend on omega; the paper says 'There is little experimental data for the parameter omega' and only gives an illustrative value (3 omega = 10^{-3}). No measurement or fit is provided, so the quantitative predictions are undetermined until omega is fixed.
assumptions (8)
  • domain assumption Yang-Mills gravity, a T4 gauge theory in flat spacetime, is the correct framework and its geometric-optics limit produces the effective metric G_munu.
    The entire paper is built on this alternative theory, cited to refs [1,2,3,7]; it is not derived here and is outside standard general relativity.
  • domain assumption The universe is homogeneous and isotropic, reducing the effective metric to the time-dependent form G_munu(t) = (B^2, -A^2, -A^2, -A^2).
    Stated in Sec 2; the cosmological principle is applied to the effective metric of Yang-Mills gravity.
  • domain assumption The matter-dominated solution has A = alpha t^{1/2}, B = beta t^{1/2} with beta = 3 alpha^{5/2} g^2 rho_o and alpha = (8 g^6 omega rho_o^3 / 9)^{1/12}.
    Imported from the HHK model [10] and stated in Eq (11); all later formulas depend on this solution, but it is not rederived in this paper.
  • domain assumption A distant galaxy of mass m obeys the Okubo equation G^{mu nu} partial_mu S partial_nu S = m^2.
    The paper derives this from an action principle in Sec 2, but the step from wave equations in Yang-Mills gravity to the Hamilton-Jacobi form relies on the geometric-optics limit from prior work.
  • ad hoc to paper Light emitted from accelerated distant galaxies obeys the massless Okubo equation G^{mu nu} partial_mu psi_e partial_nu psi_e = 0.
    Assumed in Sec 4 as the super-macroscopic extension of the eikonal equation; no derivation from the Yang-Mills Lagrangian is given.
  • ad hoc to paper The principle of limiting continuation of physical laws, including weak equivalence of non-inertial frames, connects the auxiliary frame F_e to the inertial frame F.
    Used in Sec 4 to equate covariant eikonal equations (27) and to set Eq (31); this is a heuristic principle from prior Hsu and Hsu work, not a derived theorem.
  • ad hoc to paper The velocity V_r in the Doppler transformation is identified with the dimensionless recession velocity dot r/C_o.
    Sec 4 says 'by dimensional analysis, it is natural to identify V_r...'; this identification is what turns the standard Doppler formula into a cosmological redshift prediction.
  • ad hoc to paper Matter domination is compatible with a nonzero pressure-to-energy-density ratio omega.
    C_o = (3 omega)^{1/3} requires omega > 0, while standard matter-dominated cosmologies take P approximately 0; the paper neither justifies omega > 0 nor quantifies it.
invented entities (1)
  • Auxiliary expansion frame F_e
    purpose: A non-inertial frame in which all distant galaxies are at rest, used to define the emitted frequency [k_e0/B] and to apply weak equivalence in the redshift derivation.
    The frame is explicitly said to lack well-defined space and time coordinates over all space; it is only an auxiliary construct with no independent falsifiable handle.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Exact Recession Velocity and Cosmic Redshift Based on Cosmological Principle and Yang-Mills Gravity." pith.science (2026). https://pith.science/paper/XGUABVX2

@misc{pith2026190801585,
  author       = {Pith},
  title        = {Pith review of: Exact Recession Velocity and Cosmic Redshift Based on Cosmological Principle and Yang-Mills Gravity},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XGUABVX2}},
  note         = {Machine review of arXiv:1908.01585}
}
abstract

Based on the cosmological principle and quantum Yang-Mills gravity in the super-macroscopic limit, we obtain an exact recession velocity and cosmic redshift z, as measured in an inertial frame $F\equiv F(t,x,y,z).$ For a matter-dominated universe, we have the effective cosmic metric tensor $G_{\mu\nu}(t)=(B^2(t),-A^2(t),-A^2(t),-A^2(t)), \ A\propto B\propto t^{1/2}$, where $t$ has the operational meaning of time in $F$ frame. We assume a cosmic action $S\equiv S_{cos}$ involving $G_{\mu\nu}(t)$ and derive the `Okubo equation' of motion, $G^{\mu\nu}(t)\partial_\mu S \partial_\nu S - m^2=0$, for a distant galaxy with mass $m$. This cosmic equation predicts an exact recession velocity, $\dot{r}=rH/[1/2 +\sqrt{1/4+r^2H^2/C_o^2} ]<C_o$, where $H=\dot{A}(t)/A(t)$ and $C_o=B/A$, as observed in the inertial frame $F$. For small velocities, we have the usual Hubble's law $\dot{r} \approx rH$ for recession velocities. Following the formulation of the accelerated Wu-Doppler effect, we investigate cosmic redshifts z as measured in $F$. It is natural to assume the massless Okubo equation, $G^{\mu\nu}(t)\partial_\mu \psi_e \partial_\nu \psi_e=0$, for light emitted from accelerated distant galaxies. Based on the principle of limiting continuation of physical laws, we obtain a transformation for covariant wave 4-vectors between and inertial and an accelerated frame, and predict a relationship for the exact recession velocity and cosmic redshift, $z=[(1+V_r)/(1-V_r^2)^{1/2}] - 1$, where $V_r=\dot{r}/C_o<1$, as observed in the inertial frame $F$. These predictions of the cosmic model are consistent with experiments for small velocities and should be further tested.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

15 extracted references · 15 canonical work pages

  1. [1]

    J. P. Hsu, Int. J. Mod. Phys. A, 21 5119 (2006)

    work page 2006

  2. [2]

    J. P. Hsu, Chinese Phys. C, 36 (15) 403 (2012)

    work page 2012

  3. [3]

    Hsu and J

    L. Hsu and J. P. Hsu, Space-Time Symmetry and Quantum Yang-Mills Gravity (World Scientific, 2013), Part I, pp.23-30, pp. 38-42, pp.109-123 and pp. 134-141, pp. 153-161

    work page 2013

  4. [4]

    S. H. Kim, Ph.D. Thesis, Univ. of Mass. Dartmouth (2012)

    work page 2012

  5. [5]

    E. P. Wigner, Symmetries and Reflections, Scientific Essays , (The MIT Press, 1967), pp. 52-53

    work page 1967

  6. [6]

    Dyson, in 100 Years of Gravity and Accelerated Frames, The Deepest Insight of Einstein and Yang-Mills , eds

    F. Dyson, in 100 Years of Gravity and Accelerated Frames, The Deepest Insight of Einstein and Yang-Mills , eds. Jong-Ping Hsu and Dana Fine, (World Scientific, 2005) pp. 347-351

    work page 2005

  7. [7]

    S. H. Kim and J. P. Hsu, Eur. Phys. J. Plus, 127 , 146 (2012)

    work page 2012

  8. [8]

    Weinberg, Cosmology (Oxford Univ

    S. Weinberg, Cosmology (Oxford Univ. Press, 2008), pp. 10-11, p. 40, p. 62

    work page 2008

Show all 15 references
  1. [9]

    Katz, Int

    D. Katz, Int. J. Mod. Phys. A 30 , 1550119 (2015)

    2015

  2. [10]

    J. P. Hsu, L. Hsu and D. Katz, Mod. Phys. Letters A, 33 , 1850116 (2018)

    2018

  3. [11]

    Landau and E

    L. Landau and E. Lifshitz, The Classical Theory of Fields , Addison-Wesley, 1951, pp. 268-271, pp. 312-313, pp. 336-344 and p. 350

    1951

  4. [12]

    Hsu and J

    L. Hsu and J. P. Hsu, Nuovo Cimento, 112B , 1147 (1997). Appendix

    1997

  5. [13]

    J. P. Hsu and L. Hsu, Eur. Phys. J. Plus, 128 , 74 (2013). Appendix A

    2013

  6. [14]

    T. D. Lee, Particle Physics and Introduction to Field Theory (New York, Hardwood Academic, 1981), pp. 320-333,

    1981

  7. [15]

    W. H. Huang, Global Riemannian Geometry (National Taiwan University Press, 2019, forthcoming.) Sec. 1, 1.3

    2019

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.