Invariant Gravity Research Articles

Conformal gravity in three dimensions as a gauge theory.

We show that conformally invariant gravity in three dimensions is equivalent to the Yang-Mills gauge theory of the conformal group in three dimensions, with a Chern-Simons action. This means that conformal gravity is finite and exactly soluble.

Asymptotic Freedom in the Conformal Quantum Gravity with Matter

The grand unified theory (GUT) based on the O(N) and SU(N)-gauge groups after the conformally invariant gravity being included is investigated. We calculate the one-loop gravity contributions into the renormalization group equations and study their solutions. The analysis performed show that the asymptotic freedom behaviour early established for all GUT's coupling constants is not broken by taking into account this kind of gravity. However all restrictions imposed on the GUT multiplet composition become less firmly and the physical content of the constructed models is more realistic.

Exact vacuum solution to conformal Weyl gravity and galactic rotation curves

The complete, exact exterior solution for a static, spherically symmetric source in locally conformal invariant Weyl gravity is presented. The solution includes the familiar exterior Schwarzschild solution as a special case and contains an extra gravitational potential term which grows linearly with distance. The obtained solution provides a potential explanation for observed galactic rotation curves without the need for dark matter. The solution also has some interesting implications for cosmology.

Quantum theory of two-dimensional gravity.

We discuss local O(2,1)-invariant two-dimensional gravity interacting with scalar matter fields. Quantum constraints of lapse and shift functions are obtained by demanding the conformal algebra without a center. From the constraints and the covariant conservation law, we derive the semiclassical expectation value of the energy-momentum tensor of matter.

Mass spectrum of the M 4×S D solution in Euler invariant type higher derivative gravity

The mass spectrum is computed in Euler invariant type higher derivative gravity theory in the case that the space-time is dimensionally reduced to the four-dimensional Minkowski space × D-dimensional sphere. It is shown at the linearized level that after the compactification there appear massless gravitons, massive spin-two particles, massless vectors and one massive scalar mode. All the vectors are massless and the masses of massive spin-two particles are proportional to the S D eigenvalues of the laplacian. Classical stability is shown to depend only on three parameters.

De Sitter invariant gravity coupled with matter and its cosmological consequences: Takeshi Fukuyama. Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606 and Faculty of General Education, Osaka Institute of Technology, Asahiku Omiya, Osaka 535, Japan

De Sitter invariant gravity coupled with matter and its cosmological consequences: Takeshi Fukuyama. Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606 and Faculty of General Education, Osaka Institute of Technology, Asahiku Omiya, Osaka 535, Japan

De Sitter invariant gravity coupled with matter and its cosmological consequences

A new mathematical framework for de Sitter invariant gravity is described. Gauge symmetry follows the pattern of symmetry breaking; O(4, 2) → O(4, 1) → O(3, 1). Intimate relationships between spacetime and matter are exhibited via the interaction of gravity with scalar and spinor fields. The relevance of these results to GUT cosmology is discussed. It is shown that the cosmological constant is zero after the phase transition.

On the calculability of Newton's constant and the renormalizability of scale invariant quantum gravity

We argue that Newton's constant is not unambiguossly calculable in any non-finite pure matter theory. In finite, supersymmetric, conformally invariant theories it is calculable in terms of scalar expectation values. Implications for the renormalizability of scale invariant and conformally invariant quantum gravity are discussed.

On a dilatation-invariant framework for spin-1/2 composite gravity

In analogy to the representation of Einstein’sGL 4,R invariant gravity in terms of the tetrad fields with an additionalSO 3,1 invariance—interpretable as a nonlinear realization induced by a symmetry breakdown ofGL 4,R —a representation of the tetrad by spin-1/2SU 2 fields is proposed. The dilatation-invariant dynamical framework with the effective multifactorial group structureG 2 =GL 4,R ⊗O 3,1 ⊗SU 2 contains only composite gauge fields. Motivated by the nested hierarchical structure ofG 2, we propose a «unification by proliferation» brought about by nonlinear realizations which are triggered by a breakdown chainGL 4,R →SO 3,1 →SU 2 .

Remarks on a class of almost trivial solutions of the gravitational field equation: K. Kraus. Institute for Theoretical Physics Universität Marburg, Marburg, Germany

The mass spectrum is computed in Euler invariant type higher derivative gravity theory in the case that the space-time is dimensionally reduced to the four-dimensional Minkowski space × D-dimensional sphere. It is shown at the linearized level that after the compactification there appear massless gravitons, massive spin-two particles, massless vectors and one massive scalar mode. All the vectors are massless and the masses of massive spin-two particles are proportional to the SD eigenvalues of the laplacian. Classical stability is shown to depend only on three parameters.