Conformal and Affine Hamiltonian Dynamics of General Relativity

TL;DR

This paper develops a Hamiltonian formulation of General Relativity incorporating conformal and affine symmetries, explaining cosmic acceleration, energy hierarchies, and early Universe phenomena through vacuum energy and gravitational waves.

Contribution

It introduces a novel Hamiltonian approach using Dirac scalar dilaton and Maurer-Cartan forms, linking symmetry, vacuum energy, and cosmological observations.

Findings

Good description of supernova luminosity distance-redshift relation

Hierarchy of Universe energy scales derived from Planck epoch principles

Single-component strong gravitational waves from Maurer-Cartan invariance

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.