^{μ ν}rather than the metric tensor g

_{μ ν}. The corresponding Lagrangian function, denoted as L

_{R}, is realized by a polynomial expression of the Ricci 4-scalar R ≡g

_{μ ν}R

^{μ ν}and of the quadratic curvature 4-scalar ρ ≡R

^{μ ν}R

_{μ ν}. The Lagrangian variational principle applies both to vacuum and non-vacuum cases and for its validity it demands a non-vanishing, and actually also positive, cosmological constant Λ >0 . Then, by implementing the deDonder-Weyl formalism, the physical conditions for the existence of a manifestly-covariant Hamiltonian structure associated with such a Lagrangian formulation are investigated. As a consequence, it is proved that the Ricci tensor can obey a Hamiltonian dynamics which is consistent with the solutions predicted by the Einstein field equations.

Read More