On the cosmological constant in the deformed Einstein-Cartan gauge gravity in De Donder-Weyl Hamiltonian formulation

TL;DR

This paper proposes a modified gravity theory based on the De Donder-Weyl Hamiltonian formulation that predicts a vanishing total energy-momentum and offers a natural explanation for the small observed cosmological constant.

Contribution

It introduces Covariant Canonical Gauge Gravity (CCGG), a quadratic extension of Einstein-Cartan theory, which predicts a zero total energy-momentum and explains the smallness of the cosmological constant.

Findings

Predicts a vanishing total energy-momentum of space-time and matter.

Shows the observed cosmological constant is a small correction from deviations and dynamical effects.

Provides a natural resolution to the cosmological constant problem.

Abstract

A modification of the Einstein-Hilbert theory, the Covariant Canonical Gauge Gravity (CCGG), leads to a cosmological constant that represents the energy of the space-time continuum when deformed from its (A)dS ground state to a flat geometry. CCGG is based on the canonical transformation theory in the De Donder-Weyl (DW) Hamiltonian formulation. That framework modifies the Einstein-Hilbert Lagrangian of the free gravitational field by a quadratic Riemann-Cartan concomitant. The theory predicts a total energy-momentum of the system of space-time and matter to vanish, in line with the conjecture of a "Zero-Energy-Universe" going back to Lorentz (1916) and Levi-Civita (1917). Consequently a flat geometry can only exist in presence of matter where the bulk vacuum energy of matter, regardless of its value, is eliminated by the vacuum energy of space-time.% $\lambda_0$. The observed cosmological constant $\Lambda_{\mathrm{obs}}$ is found to be merely a small correction %of the order $10^{-120} \,\lambda_0$ attributable to deviations from a flat geometry and effects of complex dynamical geometry of space-time, namely torsion and possibly also vacuum fluctuations of matter and space-time. That quadratic extension of General Relativity, anticipated already in 1918 by Einstein \cite{einstein18}, thus provides a significant and natural contribution to resolving the %$120$ orders of magnitude miss-estimate called the "cosmological constant problem".