Conformal and Affine Hamiltonian Dynamics of General Relativity

Abstract

The Hamiltonian approach to the General Relativity is formulated as a joint nonlinear realization of conformal and affine symmetries by means of the Dirac scalar dilaton and the Maurer-Cartan forms. The dominance of the Casimir vacuum energy of physical fields provides a good description of the type Ia supernova luminosity distance--redshift relation. Introducing the uncertainty principle at the Planck's epoch within our model, we obtain the hierarchy of the Universe energy scales, which is supported by the observational data. We found that the invariance of the Maurer-Cartan forms with respect to the general coordinate transformation yields a single-component strong gravitational waves. The Hamiltonian dynamics of the model describes the effect of an intensive vacuum creation of gravitons and the minimal coupling scalar (Higgs) bosons in the Early Universe.

37 pages, version submitted to Gen. Rel. Grav

References in corpus (6)

• The Standard Model Higgs boson as the inflaton
• Constraining f(R) Gravity as a Scalar Tensor Theory
• Higgs-Dilaton Cosmology: From the Early to the Late Universe
• Scale-invariant alternatives to general relativity
• Conformal Hamiltonian Dynamics of General Relativity
• Conformal Cosmological Model Parameters with Distant SNe Ia Data: "gold" and "silver"

Cited by in corpus (5)

• Will there be future deceleration? A study of particle creation mechanism in non-equilibrium thermodynamics
• Conformally Coupled General Relativity
• Basic issues of conservative approaches to quantum theory of gravity
• Inflationary solutions in the simplest gravity model with conformal symmetry
• Von Neumann's Quantization of General Relativity