Covariant Canonical Gauge Gravitation and Cosmology

Abstract

The covariant canonical transformation theory applied to the relativistic Hamiltonian theory of classical matter fields in dynamical space-time yields a novel (first order) gauge field theory of gravitation. The emerging field equations necessarily embrace a quadratic Riemann term added to Einstein's linear equation. The quadratic term endows space-time with inertia generating a dynamic response of the space-time geometry to deformations relative to (Anti) de Sitter geometry. A "deformation parameter" is identified, the inverse dimensionless coupling constant governing the relative strength of the quadratic invariant in the Hamiltonian, and directly observable via the deceleration parameter $q_0$. The quadratic invariant makes the system inconsistent with Einstein's constant cosmological term, $\Lambda =\mathrm{const}$. In the Friedman model this inconsistency is resolved with the scaling ansatz of a "cosmological function", $\Lambda (a)$, where $a$ is the scale parameter of the FLRW metric. %Moreover, the strain generated by the quadratic term turns out to act as a geometrical stress. The cosmological function can be normalized such that with the $\Lambda$ CDM parameter set the present-day observables, the Hubble constant and the deceleration parameter, can be reproduced. %We analyze the asymptotics of the such normalized Friedman equations with respect to both, the fundamental parameters (coupling constants) and the scale $a$. With this parameter set we recover the dark energy scenario in the late epoch. The proof that inflation in the early phase is caused by the "geometrical fluid" representing the inertia of space-time is yet pending, though.

arXiv commentMinor error corrected with no impact on results, 10 pages, one figure

References in corpus (10)

• Planck 2015 results. XIII. Cosmological parameters
• The Cosmological Constant
• Modified gravity models of dark energy
• Covariant Hamiltonian Field Theory
• Canonical Transformation Path to Gauge Theories of Gravity
• de Sitter Relativity: a New Road to Quantum Gravity?
• Quadratic curvature theories formulated as Covariant Canonical Gauge theories of Gravity
• Asymmetry in the reconstructed deceleration parameter
• Energy transfer from space-time into matter and a bouncing inflation from Covariant Canonical Gauge theory of Gravity
• The picture of our universe: A view from modern cosmology

Cited by in corpus (8)

• Inflation from fermions with curvature-dependent mass
• Torsional dark energy in quadratic gauge gravity
• Dark energy and inflation invoked in CCGG by locally contorted space-time
• Torsion driving cosmic expansion
• Covariant canonical gauge theory of gravitation for fermions
• On the cosmological constant in the deformed Einstein-Cartan gauge gravity in De Donder-Weyl Hamiltonian formulation
• Rigorous derivation of dark energy and inflation as geometry effects in Covariant Canonical Gauge Gravity
• Gauge theory of Gravity based on the correspondence between the $1^{st}$ and the $2^{nd}$ order formalisms