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We discuss a model of dark matter consisting of high energy anti-electron-neutrinos with leptonic force, which is produced by the conserved leptonic charge $g_\ell$ associated with Lee-Yang's $U_1$ gauge symmetry. Based on particle-cosmology for early universe, the high energy neutrino (HEN) model of dark matter assumes that the neutron decay processes, $n\to p^+ + e^- +\ov{\nu}_e$, dominate the epoch after the creation, collision and confinement processes of quarks and antiquarks in the beginning. The HEN model implies the following results: There are almost equal numbers of electrons, protons and anti-electron-neutrinos dominated the matter cosmos. There are unobservable and ubiquitous anti-electron-neutrinos $\ov{\nu}_e$ with leptonic charge $g_\ell$ in the universe. Although the total mass of anti-electron-neutrino dark matter is negligible in the universe, its enhanced gravitational and leptonic forces could lead to the observed flat rotation curves due to relativistic $\ov{\nu}_e$, whose static force involves a factor $E_\nu/m_\nu\approx 10^6$. We estimate the leptonic charge to be $g_\ell \approx 7 \times 10^{-21}$. The model predicts that the anti-electron-neutrino dark matter can interact with cosmic-ray protons to produce positrons, i.e. $\ov{\nu}_e + p^+ \to e^+ +n$, through weak interaction of the unified electroweak theory. The anti-electron-neutrino dark matter sheds light on the Alpha Magnetic Spectrometer (AMS) experiment, which has detected the intriguing excess of cosmic-ray positrons over what is expected. The HEN model of dark matter suggests an experimental test of the new Lee-Yang force between electrons by using modern precision Cavendish experiment., Comment: 25 pages

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} ], Comment: 7 pages, to be published in Chinese Physics C. (2019)

Based on particle physics, the fundamental CPT invariance suggests a Big Jets model for the beginning of the universe, in which two oppositely directed jets evolved into a gigantic "matter half-universe" and a gigantic "antimatter half-universe" after annihilation and decay processes. In the geometric-optics limit, quantum Yang-Mills gravity with $T_4$ translational gauge symmetry in flat spacetime leads to an effective metric tensor in the Hamilton-Jacobi equation for macroscopic objects. This effective metric tensor does not exist in the wave equations of quantum particles. For cosmological expansion, we assume that an "effective metric tensor" for spacetime geometry based on Yang-Mills gravity corresponds to the usual FLRW form. Dynamical equations of expansion for the matter half-universe are obtained and solved. The time-dependent scale factors and the estimated age of the universes, $t^{YM}_o \approx 15.3 \times 10^9 yr$, based on Yang-Mills gravity are consistent with experiments. CPT invariance implies that the same evolution process and dynamics of cosmic expansion also hold for the distant `antimatter half-universe.', 9 pages

Based on baryon charge conservation and a generalized Yang-Mills symmetry for Abelian (and non-Abelian) groups, we discuss a new baryonic gauge field and its linear potential for two point-like baryon charges. The force between two point-like baryons is repulsive, extremely weak and independent of distance. However, for two extended baryonic systems, we have a dominant linear force α r. Thus, only in the later stage of the cosmic evolution, when two baryonic galaxies are separated by an extremely large distance, the new repulsive baryonic force can overcome the gravitational attractive force. Such a model provides a gauge-field-theoretic understanding of the late-time accelerated cosmic expansion. The baryonic force can be tested by measuring the accelerated Wu-Doppler frequency shifts of supernovae at different distances.

Based on the limiting continuation of Lorentz-Poincaré invariance, we propose an alternative formulation of the generalized Planck distribution for inertial and noninertial frames. The Lorentz invariant Planck distribution law leads to a new physical interpretation of the dipole anisotropy of the Cosmic Microwave Background. The Big Jets model predicts a distant ‘antimatter blackbody,’ whose radiations could make 50% of the sky very slightly warmer than the isotropic CMB temperature TCMB with a cosine function. The other 50% of the sky has the same isotropic temperature TCMB. Thus, we could have a pseudo-dipole anisotropy because the microwaves emitted from the antimatter blackbody are totally absorbed by our matter blackbody. We suggest that accurate data of satellite experiments might be used to search for the pseudo-dipole anisotropy and the missing half of the antimatter universe.

Within the gauge symmetry framework, the [Formula: see text] symmetry of electrodynamics is violated in the presence of gravity with spacetime translational gauge symmetry in inertial frames. For a light ray, an eikonal equation with effective metric tensors is derived in the geometric-optics limit. Under these conditions, the angle of the deflection of light by the sun is calculated to be [Formula: see text] in inertial frames without requiring a gauge condition such as [Formula: see text]. In contrast, if the theory is [Formula: see text] gauge invariant, one can impose the gauge condition [Formula: see text] in the derivation of the eikonal equation. In this case, one obtains a slightly different effective metric tensor and a different angle of deflection [Formula: see text]. However, because the precision of experiments in the last century using optical frequencies has been no better than (10–20)% due to large systematic errors, one cannot unambiguously rule out the result [Formula: see text]. We hope that the precision of these data can be improved in order to test Yang–Mills gravity.

The conservation of lepton number is assumed to be associated with a general Yang-Mills symmetry. New transformations involve (Lorentz) vector gauge functions and characteristic phase functions, and they form a group. General Yang-Mills fields are associated with new fourth-order equations and linear potentials. Lepton self-masses turn out to be finite and proportional to the inverse of lepton masses, which implies that neutrinos should have non-zero masses. Thus, general Yang-Mills symmetry could provide an understanding of neutrino oscillations and suggests that neutrinos with masses and very weak leptonic force may play a role in dark matter., Comment: 9 pages, to be published in Modern Physics Letters A (2016)

In Yang-Mills gravity based on flat space-time, the eikonal equation for a light ray is derived from the modified Maxwell’s wave equations in the geometric-optics limit. One obtains a Hamilton-Jacobi type equation, GLµv∂µΨ∂vΨ = 0 with an effective Riemannian metric tensor GLµv. According to Yang-Mills gravity, light rays (and macroscopic objects) move as if they were in an effective curved space-time with a metric tensor. The deflection angle of a light ray by the sun is about 1.53″ for experiments with optical frequencies ≈ 1014Hz. It is roughly 12% smaller than the usual value 1.75″. However, the experimental data in the past 100 years for the deflection of light by the sun in optical frequencies have uncertainties of (10-20)% due to large systematic errors. If one does not take the geometric-optics limit, one has the equation, GLµv[∂µΨ∂vΨcosΨ+ (∂µ∂vΨ)sinΨ] = 0, which suggests that the deflection angle could be frequency-dependent, according to Yang-Mills gravity. Nowadays, one has very accurate data in the radio frequencies ≈ 109Hz with uncertainties less than 0.1%. Thus, one can test this suggestion by using frequencies ≈ 1012 Hz, which could have a small uncertainty 0.1% due to the absence of systematic errors in the very long baseline interferometry.

Within Yang-Mills gravity with translation group $T(4)$ in flat space-time, the invariant action involving quadratic translation gauge-curvature leads to quadrupole radiations which are shown to be consistent with experiments. The radiation power turns out to be the same as that in Einstein's gravity to the second-order approximation. We also discuss an interesting physical reason for the accelerated cosmic expansion based on the long-range Lee-Yang force of $U_{b}(1)$ gauge field associated with the established conservation law of baryon number. We show that the Lee-Yang force can be related to a linear potential $\propto r$, provided the gauge field satisfies a fourth-order differential equation. Furthermore, we consider an experimental test of the Lee-Yang force related to the accelerated cosmic expansion. The necessity of generalizing Lorentz transformations for accelerated frames of reference and accelerated Wu-Doppler effects are briefly discussed., 19 pages

A new translation gauge theory of gravity in flat space-time with a new Yang-Mills action involves quadratic gauge curvature and fermions. The theory shows that the presence of an “effective Riemannian metric tensor” for the motions of classical particles and light rays is probably the manifestation of the translation gauge symmetry in flat physical space-time. In the post-Newtonian approximation of the tensor gauge field produced by the energymomentum tensor, the results are shown to be consistent with classical tests of gravity and with the quadrupole radiations of binary pulsars.

We discuss ideas and problems regarding classical and quantum gravity, gauge theory of gravity, and space–time transformations between accelerated frames. Both Einstein's theory of gravity and Yang–Mills theory are gauge invariant. The invariance principles are at the very heart of our understanding of the physical world. This paper attempts to survey the development and to reveal problems and limitations of various formulations to gravitational and Yang–Mills fields, and to space–time transformations of accelerated frames. Gravitational force and accelerated frames are two ingredients in Einstein's thought in the period around 1907. Accelerated frames are difficult to define and are not well developed. However, one cannot claim to have a complete understanding of the physical world, if one understands flat space–time physics only from the viewpoint of the special class of inertial frames and ignores the vast class of noninertial frames. The paper highlights three aspects: (1) ideas of gravity as a Yang–Mills field, first discussed by Utiyama; (2) problems of quantum gravity, discussed by Feynman, Dyson and others; (3) space–time properties and the physics of fields and particles in accelerated frames of reference. These unfulfilled aspects of Einstein and Yang–Mills' profound thoughts present a challenge to physicists and mathematicians in the 21st century.

In 1955, Lee and Yang discussed a new massless gauge field based on the established conservation of baryon number. They predicted the existence of a repulsive force between baryonic matter, just as the conservation of electron–lepton number was later shown to imply the existence of a repulsive force between electrons. Although Eötvös experiments showed the force to be undetectably small at that time, such a force may be related to the dark-energy-induced acceleration of the expansion of the universe. If the gauge invariant Lagrangian involves a spacetime derivative of the field strength, the resultant potential has properties similar to that of the "dark energy" implied by the cosmological constant in the Einstein's equation.

Based on Lorentz and Poincaré invariance, we discuss reference frames with constant-linear-accelerations and their generalized space–time transformations with minimal departure from the Lorentz transformations. The requirement of limiting four-dimensional symmetry of the Lorentz and Poincaré groups assures that the generalized transformations reduce to the Lorentz transformations in the limit of zero acceleration. This suggests that the space–time coordinates xμ of accelerated frames are as meaningful as those of inertial frames. A flexibility and "gauge invariance" of the time for noninertial frames are discussed. These properties and the changes in the space–time of accelerated frames are shown graphically, including singularities and horizons. Physical implications of various accelerated transformations related to accelerated lifetime or decay-length dilations are predicted for experimental test.

We discuss a confining model for charmonium in which the attractive force are derived from a new type of gauge field equation with a generalized $SU_3$ gauge symmetry. The new gauge transformations involve non-integrable phase factors with vector gauge functions $\om^a_{\mu}(x)$. These transformations reduce to the usual $SU_3$ gauge transformations in the special case $\om^a_\mu(x) = \p_\mu \xi^a(x)$. Such a generalized gauge symmetry leads to the fourth-order equations for new gauge fields and to the linear confining potentials. The fourth-order field equation implies that the corresponding massless gauge boson has non-definite energy. However, the new gauge boson is permanently confined in a quark system by the linear potential. We use the empirical potentials of the Cornell group for charmonium to obtain the coupling strength $f^2/(4\pi) \approx 0.19$ for the strong interaction. Such a confining model of quark dynamics could be compatible with perturbation. The model can be applied to other quark-antiquark systems., Comment: 6 pages

A generalization of the usual gauge symmetry leads to fourth-order gauge field equations, which imply a new constant force independent of distances. The force associated with the new $U_1$ gauge symmetry is repulsive among baryons. Such a constant force based on baryon charge conservation gives a field-theoretic understanding of the accelerated cosmic-expansion in the observable portion of the universe dominated by baryon galaxies. In consistent with all conservation laws and known forces, a simple rotating `dumbbell model' of the universe is briefly discussed., 15 pages, to be published in Modern Physics Letters A, 29 (2014)

Thim measured the transverse Doppler shift using a system consisting of a stationary antenna and pickup, in addition to a number of intermediate antennas mounted on the rim of a rotating disk. No such shift was detected, although the experiment should have had enough sensitivity to measure it, as predicted by the Lorentz transformations. However, using the Lorentz transformations to analyze the results of experiments involving circular motion, while commonly done, is inappropriate because such an analysis involves non-inertial frames, which are outside the range of validity of special relativity. In this paper, we re-analyze Thim's experiment using exact rotational space-time transformations, finding that his null result is consistent with theoretical predictions., 8 pages

We discuss a confining model for quark-antiquark system with a new color $SU_3$ gauge symmetry. New gauge transformations involve non-integrable phase factors and lead to the fourth-order gauge field equations and a linear potential. The massless gauge bosons have non-definite energies, which are not observable because they are permanently confined in quark systems by the linear potential. We use the empirical potentials of charmonium to determine the coupling strength of the color charge $g_s$ and find $g_s^2/(4\pi) \approx 0.2.$ We discuss Feynman-Dyson rules for the confining quark model, which involve propagators with poles of order 2 associated with new gauge fields. The confining quark model may be renormalizable by power counting and compatible with perturbation theory., Comment: 10 pages