A first-order approach to conformal gravity (original) (raw)
Related papers
2013
This is the first of three papers on Conformal General Relativity (CGR), which differs from Einstein's General Relativity (GR) in that it requires action-integral invariance under local scale transformations in addition to general coordinate transformations. The theory is here introduced in the semiclassical approximation as a preliminary approach to a quantum theoretical implementation. The idea of a conformal-invariant extension of GR was introduced by Weyl in 1919. For several decades it had little impact, as CGR implies that all fields are massless. Today this does not appear to be an unsurmountable difficulty since nonzero mass parameters may result from the spontaneous breakdown of conformal symmetry. The theory leads to very interesting results and predictions: 1) the spontaneous breakdown of conformal symmetry is only possible in a 4D-spacetime with small negative curvature; 2) CGR requires the introduction of a ghost scalar field σ(x) invested with geometric meaning and a physical scalar field ϕ(x) of zero mass, both of which have nonzero vacuum expectation values; 3) in order to preserve S-matrix unitarity, σ(x) and ϕ(x) must interact in such a way that the total energy density is bounded from below; 4) this interaction makes ϕ(x) behave like a Higgs field of varying mass, which is capable of promoting a huge energy transfer from geometry to matter identifiable as the big bang; 5) in the course of time, the Higgs boson mass becomes a constant and CGR converges to GR.
The Conformal Universe I: Physical and Mathematical Basis of Conformal General Relativity
This is the first of three papers on Conformal General Relativity (CGR), which differs from Einstein's General Relativity (GR) in that it requires action-integral invariance under local scale transformations in addition to general coordinate transformations. The theory is here introduced in the semiclassical approximation as a preliminary approach to a quantum theoretical implementation. The idea of a conformal-invariant extension of GR was introduced by Weyl in 1919. For several decades it had little impact, as CGR implies that all fields are massless. Today this does not appear to be an unsurmountable difficulty since nonzero mass parameters may result from the spontaneous breakdown of conformal symmetry. The theory leads to very interesting results and predictions: 1) the spontaneous breakdown of conformal symmetry is only possible in a 4D-spacetime with small negative curvature; 2) CGR requires the introduction of a ghost scalar field σ(x) invested with geometric meaning and a physical scalar field ϕ(x) of zero mass, both of which have nonzero vacuum expectation values; 3) in order to preserve S-matrix unitarity, σ(x) and ϕ(x) must interact in such a way that the total energy density is bounded from below; 4) this interaction makes ϕ(x) behave like a Higgs field of varying mass, which is capable of promoting a huge energy transfer from geometry to matter identifiable as the big bang; 5) in the course of time, the Higgs boson mass becomes a constant and CGR converges to GR.
Electronic Journal of Theoretical Physics
This is the second of three papers on Conformal General Relativity (CGR). The conformal group is introduced here as the invariance group of the partial order of causal events in nD spacetime. Its general structure, discrete symmetries and field representations are described in detail. The spontaneous breakdown of conformal symmetry is then discussed and the role played by a ghost scalar field and a physical scalar field in 4D spacetime are evidenced. Kinematic-, conformal-and proper-time hyperbolic coordinates are introduced in a negatively curved Milne spacetime for the purpose of providing three different but equivalent representations of CGR. The first of these is grounded in a Riemannian manifold and is manifestly conformal invariant, the second is grounded in a conformally connected Cartan manifold but its conformal invariance is hidden, the third is grounded in the Riemannian manifold of the Milne spacetime and has the formal structure of General Relativity (GR). The relation between CGR and standard inflationary cosmology is also briefly discussed. Lastly, in view of the detailed study of Higgs-field dynamics carried out in the third paper, the action integrals, motion equations and total energy-momentum tensors of the Higgs field interacting with the dilation field are described in the three representations mentioned above.
The role of conformal symmetry in gravity and the standard model
Classical and Quantum Gravity, 2016
In this paper we consider conformal symmetry in the context of manifolds with general affine connection. We extend the conformal transformation law of the metric to a general metric compatible affine connection, and find that it is a symmetry of both the geodesic equation and the Riemann tensor. We derive the generalised Jacobi equation and Raychaudhuri equation and show that they are both conformally invariant. Using the geodesic deviation (Jacobi) equation we analyse the behaviour of geodesics in different conformal frames. Since we find that our version of conformal symmetry is exact in classical pure Einstein's gravity, we ask whether one can extend it to the standard model. We find that it is possible to write conformal invariant lagrangians in any dimensions for vector, fermion and scalar fields, but that such lagrangians are only gauge invariant in four dimensions. Provided one introduces a dilaton field, gravity can be conformally coupled to matter.
On the Conformal Unity between Quantum Particles and General Relativity
OALib, 2017
I consider the standard model, together with a preon version of it, to search for unifying principles between quantum particles and general relativity. Argument is given for unified field theory being based on gravitational and electromagnetic interactions alone. Conformal symmetry is introduced in the action of gravity with the Weyl tensor. Electromagnetism is geometrized to conform with gravity. Conformal symmetry is seen to improve quantization in loop quantum gravity. The Einstein-Cartan theory with torsion is analyzed suggesting structure in spacetime below the Cartan scale. A toy model for black hole constituents is proposed. Higgs metastability hints at cyclic conformal cosmology.
Hamiltonian analysis of curvature-squared gravity with or without conformal invariance
Physical Review D, 2014
We analyze gravitational theories with quadratic curvature terms, including the case of conformally invariant Weyl gravity, motivated by the intention to find a renormalizable theory of gravity in the ultraviolet region, yet yielding general relativity at long distances. In the Hamiltonian formulation of Weyl gravity, the number of local constraints is equal to the number of unstable directions in phase space, which in principle could be sufficient for eliminating the unstable degrees of freedom in the full nonlinear theory. All the other theories of quadratic type are unstable-a problem appearing as ghost modes in the linearized theory. We find that the full projection of the Weyl tensor onto a three-dimensional hypersurface contains an additional fully traceless component, given by a quadratic extrinsic curvature tensor. A certain inconsistency in the literature is found and resolved: when the conformal invariance of Weyl gravity is broken by a cosmological constant term, the theory becomes pathological, since a constraint required by the Hamiltonian analysis imposes the determinant of the metric of spacetime to be zero. In order to resolve this problem by restoring the conformal invariance, we introduce a new scalar field that couples to the curvature of spacetime, reminiscent of the introduction of vector fields for ensuring the gauge invariance.
On Conformally Coupled General Relativity
EPJ Web of Conferences
A gravity model based on the conformal symmetry is presented. To specify the structure of the general coordinate transformations the Ogievetsky theorem is applied. The nonlinear symmetry realization approach is used. Canonical quantization is performed with the use of reparameterizationinvariant time and the Arnowitt-Deser-Misner foliation. Renormalizability of the constructed quantum gravity model is discussed.