Interaction Between Massive and Massless Gravitons by Perturbing Topological Field Theory

We test the Wu gauge theory of gravity with massive gravitons in the perturbing topological field theory framework.We show that the computation of the correlation function between massive and massless gravitons is reported up to 4-loop and appears to be unaffected by radiative correction.This result ensures the stability of the linking number between massive and massless gravitons with respect to the local perturbation,a result with potential wider applications in cosmology.     

Gauge theories of weak and strong gravity

A review of some recent papers on gauge theories of weak and strong gravity is presented. For weak gravity, SL(2, C) gauge theory along with tetrad formulation is described which yields massless spin-2 gauge fields (quanta gravitons). Next a unified SL(2n,C) model is discussed along with Higgs fields. Its internal symmetry is SU(n). The free field solutions after symmetry breaking yield massless spin-1 (photons) and spin-2 (gravitons) gauge fields and also massive spin-1 and spin-2 bosons. The massive spin-2 gauge fields are responsible for short range superstrong gravity. Higgs-fermion interaction can lead to baryon and lepton number non-conservation. The relationship of strong gravity with other forces is also briefly considered.     

Cosmic Acceleration in a Model of Interacting Massive Gravitons Dark Energy

We propose an alternative understanding of gravity, resulting from the extension of N. Wu’s gauge theory of gravity with massive gravitons, which are minimally coupled to massless gravitons. Based on this, we derive the equations of state for massive gravitons. We study the dynamics of these massive gravitons in a flat, homogeneous and isotropic Friedmann-Robertson-Walker (FRW) universe. We calculate the critical points of the massive graviton dark energy interacting with background perfect fluid. These calculations may have crucial implications for the massive gravitons and dark energy theories. They could, therefore, have important repercussions for current cosmological problems.     

Spontaneous lorentz breaking and massive gravity

Theories with an extra spin-two field coupled to gravity admit a massive phase with broken Lorentz symmetry. While the equivalence principle is respected, the Newtonian potentials are in general modified, but they may be protected by a scale symmetry of the coupling term. The gravitational waves phenomenology is quite rich: two gravitons, one massive and one massless, oscillate and propagate with distinct velocities, different from the speed of light. A time of flight difference between gravitons and photons from a common source would provide a clear signal of this theory.     

Renormalizable Quantum Gauge Theory of Gravity

The quantum gravity is formulated based on the principle of local gauge invariance. The model discussed in this paper has local gravitational gauge symmetry, and gravitational field is represented by gauge field. In the leading-order approximation, it gives out classical Newton's theory of gravity. In the first-order approximation and for vacuum, it gives out Einstein's general theory of relativity. This quantum gauge theory of gravity is a renormalizable quantum theory.     

Renormalizable Quantum Gauge Theory of Gravity

The quantum gravity is formulated based on the principle of local gauge invariance. The model discussedin this paper has local gravitational gauge symmetry, and gravitational field is represented by gauge field. In the leading-order approximation, it gives out classical Newton‘s theory of gravity. In the first-order approximation and for vacuum,it gives out Einstein‘s general theory of relativity. This quantum gauge theory of gravity is a renormalizable quantumtheory.     

Quantum Gauge General Relativity

Based on gauge principle, a new model on quantum gravity is proposed in the frame work of quantum gauge theory of gravity. The model has local gravitational gauge symmetry, and the field equation of the gravitational gauge field is just the famous Einstein‘s field equation. Because of this reason, this model is called quantum gauge general relativity, which is the consistent unification of quantum theory and general relativity. The model proposed in this paper is a perturbatively renormalizable quantum gravity, which is one of the most important advantage of the quantum gauge general relativity proposed in this paper. Another important advantage of the quantum gauge general relativity is that it can explain both classical tests of gravity and quantum effects of gravitational interactions, such as gravitational phase effects found in COW experiments and gravitational shielding effects found in Podkletnov experiments.     

Gravitational Gauge Interactions of Scalar Field

Quantum gauge theory of gravity is formulated based on gauge principle. Because the Lagrangian has strict local gravitational gauge symmetry, gravitational gauge theory is a perturbatively renormalizable quantum theory. Gravitational gauge interactions of scalar field are studied in this paper. In quantum gauge theory of gravity, scalar field minimal couples to gravitational field through gravitational gauge covariant derivative. Comparing the Lagrangian for scalar field in quantum gauge theory of gravity with the corresponding Lagrangian in quantum fields in curved space-time, the definition for metric in curved space-time in geometry picture of gravity can be obtained, which is expressed by gravitational gauge field. In classical level, the Lagrangian and Hamiltonian approaches are also discussed.     

Gravitational Gauge Interactions of Scalar Field

Quantum gauge theory of gravity is formulated based on gauge principle. Because the Lagrangian hasstrict local gravitational gauge symmetry, gravitational gauge theory is a perturbatively renormalizable quantum theory.Gravitational gauge interactions of scalar field are studied in this paper. In quantum gauge theory of gravity, scalar fieldminimal couples to gravitational field through gravitational gauge covariant derivative. Comparing the Lagrangian forscalar field in quantum gauge theory of gravity with the corresponding Lagrangian in quantum fields in curved space-time, the definition for metric in curved space-time in geometry picture of gravity can be obtained, which is expressedby gravitational gauge field. In classical level, the Lagrangian and Hamiltonian approaches are also discussed.     

A new gravitational model for dark energy

A new gravitational model for dark energy is presented based on the model of de Sitter gauge theory of gravity.In the model,in addition to the cosmological constant,the homogeneous and isotropic torsion and its coupling with curvature play an important role for dark energy.The model may supply the universe with a natural transit from decelerating expansion to accelerating expansion.     

A new gravitational model for dark energy

A new gravitational model for dark energy is presented based on the model of de Sitter gauge theory of gravity. In the model, in addition to the cosmological constant, the homogeneous and isotropic torsion and its coupling with curvature play an important role for dark energy. The model may supply the universe with a natural transit from decelerating expansion to accelerating expansion.     

Effective theory for dark matter and a new force in the dark matter sector

An effective theory for dark matter has recently been proposed. The key assumption is that the dark matter particle which is a Dirac fermion is protected from decaying by a global U(1) symmetry. We point out that quantum gravity effects will violate this symmetry and that the dark matter candidate thus decays very fast. In order to solve that problem, we propose to consider a local gauge symmetry which implies a new force in the dark matter sector. It is likely that this new local U(1) symmetry will need to be spontaneously broken leading for a range of the parameters of the model to a Sommerfeld enhancement of the annihilation cross sections which is useful to explain the Pamela and ATIC results using a weakly interacting massive particle with a mass in the TeV range.     

Gravitational Shielding Effect in Gauge Theory of Gravity

In 1992, E.E. Podkletnov and R. Nieminen found that under certain conditions, ceramic superconductor with composite structure reveals weak shielding properties against gravitational force. In classical Newton's theory of gravity and even in Einstein's general theory of gravity, there are no grounds of gravitational shielding effects. But in quantum gauge theory of gravity, the gravitational shielding effects can be explained in a simple and natural way. In quantum gauge theory of gravity, gravitational gauge interactions of complex scalar field can be formulated based on gauge principle. After spontaneous symmetry breaking, if the vacuum of the complex scalar field is not stable and uniform, there will be a mass term of gravitational gauge field. When gravitational gauge field propagates in this unstable vacuum of the complex scalar field, it will decays exponentially, which is the nature of gravitational shielding effects. The mechanism of gravitational shielding effects is studied in this paper, and some main properties of gravitational shielding effects are discussed.     

On the induced cosmological term in quantum gravity

Tadpole diagrams where zero-momentum gravitons couple to massive matter loops lead to divergences which are not a consequence of infinite momentum integrals, but of the masslessness of the gravitons. It is shown that there exists no definition of these diagrams consistent with the Ward identities. They can be eliminated by an appropriate gauge choice, but then the BRS symmetry is spontaneously broken. Also in the scalar-tensor, conformally invariant formulation of quantum gravity, the tadpole problem does survive. The tadpole diagrams can, however, be cancelled by a cosmological counter-term. In that case, the Ward identities are satisfied.     

Gravity from local Lorentz violation

In general relativity, gravitational waves propagate at the speed of light, and so gravitons are massless. The masslessness can be traced to symmetry under diffeomorphisms. However, another elegant possibility exists: masslessness can instead arise from spontaneous violation of local Lorentz invariance. We construct the corresponding theory of gravity. It reproduces the Einstein-Hilbert action of general relativity at low energies and temperatures. Detectable signals occur for sensitive experiments, and potentially profound implications emerge for our theoretical understanding of gravity. Third Award in the 2005 Essay Competition of the Gravity Research Foundation, 2005. - Ed.     

Hyperbolic Octonion Formulation of Gravitational Field Equations

In this paper, the Maxwell-Proca type field equations of linear gravity are formulated in terms of hyperbolic octonions (split octonions). A hyperbolic octonionic gravitational wave equation with massive gravitons and gravitomagnetic monopoles is proposed. The real gravitoelectromagnetic field equations are recovered and written in compact form from an octonionic potential. In the absence of charges, this reduces to the Klein-Gordon equation of motion for the massive graviton. The analogy between massive gravitational theory and electromagnetism is shown in terms of the present formulation.     

Unimodular bimode gravity and the coherent scalar-graviton field as galaxy dark matter

An explicit violation of the general gauge invariance/relativity is adopted as the origin of dark matter and dark energy in the context of gravitation. The violation of the local scale invariance alone, with the residual unimodular one, is considered. Besides the four-volume preserving deformation mode—the transverse-tensor graviton—the metric comprises a compression mode—the scalar graviton, or the systolon. A unimodular invariant and general covariant metric theory of the bimode/scalar-tensor gravity is consistently worked out. To reduce the primordial ambiguity of the theory a dynamical global symmetry is imposed, with its subsequent spontaneous breaking revealed. The static spherically symmetric case in empty space, except possibly for the origin, is studied. A three-parameter solution describing a new static space structure—the dark lacuna—is constructed. It enjoys the property of gravitational confinement, with the logarithmic potential of gravitational attraction at the periphery, and results in asymptotically flat rotation curves. Comprising a super-massive dark fracture (a scalar-modified black hole) at the origin surrounded by a cored dark halo, the dark lacunas are proposed as a prototype model of galaxies, implying an ultimate account for the distributed non-gravitational matter and putative asphericity or rotation.     

Maximal symmetry and mass generation of Dirac fermions and gravitational gauge field theory in six-dimensional spacetime

The relativistic Dirac equation in four-dimensional spacetime reveals a coherent relation between the dimensions of spacetime and the degrees of freedom of fermionic spinors. A massless Dirac fermion generates new symmetries corresponding to chirality spin and charge spin as well as conformal scaling transformations. With the introduction of intrinsic W-parity, a massless Dirac fermion can be treated as a Majorana-type or Weyl-type spinor in a six-dimensional spacetime that reflects the intrinsic quantum numbers of chirality spin. A generalized Dirac equation is obtained in the six-dimensional spacetime with a maximal symmetry. Based on the framework of gravitational quantum field theory proposed in Ref. [1] with the postulate of gauge invariance and coordinate independence, we arrive at a maximally symmetric gravitational gauge field theory for the massless Dirac fermion in six-dimensional spacetime. Such a theory is governed by the local spin gauge symmetry SP(1,5) and the global Poincar′e symmetry P(1,5)= SO(1,5) P~(1,5) as well as the charge spin gauge symmetry SU(2). The theory leads to the prediction of doubly electrically charged bosons. A scalar field and conformal scaling gauge field are introduced to maintain both global and local conformal scaling symmetries. A generalized gravitational Dirac equation for the massless Dirac fermion is derived in the six-dimensional spacetime. The equations of motion for gauge fields are obtained with conserved currents in the presence of gravitational effects. The dynamics of the gauge-type gravifield as a Goldstone-like boson is shown to be governed by a conserved energy-momentum tensor, and its symmetric part provides a generalized Einstein equation of gravity. An alternative geometrical symmetry breaking mechanism for the mass generation of Dirac fermions is demonstrated.     

可积(度量)Weyl时空中的引力和共形规范场理论

本文将纯规范概念引入共形群,构造了可积Weyl空间中包含引力、物质场和Weyl规范场的规范理论。讨论了有关物质场方程,得到惯性质量表达式m=kφ(x),说明了k的引力荷意义。利用Weyl标量场φ(x)的几何性质讨论了共形对称性自发破缺现象。这时Eins-tein引力自然产生,所有物质场获得统一的惯性标度。理论预言了Weyl矢量介子的存在,它是有质量中性介子,经典意义下不参予同物质场的相互作用。 关键词：     

Accelerated expansion of the universe filled up with the scalar gravitons

The concept of the scalar graviton as the source of the dark matter and dark energy of gravitational origin is applied to study the evolution of the isotropic homogeneous Universe. A realistic self-consistent solution to the modified pure gravity equations which correctly describes the accelerated expansion of the spatially flat Universe is found and investigated. It is argued that the scenario with the scalar gravitons filling up the Universe may emulate the LCDM model, thus reducing the true dark matter in the given context to an artifact. The text was submitted by the authors in English.