A pilot study on canonical gravity with mass dimension one fermions

TL;DR

This paper explores the interaction of mass dimension one fermions, potential dark matter candidates, with gravity using a canonical ADM formalism, deriving constraints and discussing implications for dark energy and matter in spacetime.

Contribution

It develops a canonical gravitational formulation incorporating mass dimension one fermions, including Hamiltonian and diffeomorphism constraints, and proposes a link to dark energy.

Findings

Derived classical Hamiltonian and diffeomorphism constraints with MDO fermions.

Interpreted dark matter energy density contributions in gravitational dynamics.

Proposed a condition for dark energy term in the action.

Abstract

The mass dimension one (MDO) fermionic field is built on a complete set of dual-helicity eigenspinors of the charge conjugation operator, which obeys the statistic of Fermi-Dirac. These spinors are a potential candidate for the description of dark matter. The redefinition of the dual structure of this object holds a local adjacent theory and satisfies complete Lorentz invariance. In this work, we investigate important aspects of the interaction of this fermion with gravity in the light of a canonical formulation in ADM formalism. We construct an action via tetrad fields using a manifold on a family of space-like surfaces $\Sigma_t$ that carries the MDO matter field, and additionally we propose a condition for the action to have a term associated with dark energy. We found the Hamiltonian and diffeomorphism constraints at the classical level for gravitational dynamics with the immersion of this material content in space-time, which leads us to the interpretation of the contribution of dark matter energy density, parallel to the lapse function of foliation and its directional flux of energy density in the hypersurface of manifold.