Global definition and physical interpretation of the cosmological constant

Defined as a global physical entity, the cosmological constant Λ appears here as a stationary functional of the metric, the matter (dark as well as visible) and the radiation fields. Subject to compact-support variations of the fields, δΛ=0 gives the metric, matter and radiation field equations. With this rigorous physical formulation, the empirical relation Λ≅ 2.7κρ ₀, where ρ₀ is the average energy-density of matter and radiation, follows from the spacetime average of κ (L−g^μν ∂L/∂g^μν) through the observable four-volume of the Universe on the homogeneity scale (∼100 Mpc), where L is the Lagrangian of the matter and radiation fields. Hence, the notion of negative-pressure dark energy is obviated in favor of an energy-density relationship for the cosmological constant that derives from the physical principle δΛ=0. Moreover, this formulation can be employed practically to rule out certain common-suspect free fields as the dominant component of dark matter. In particular, it is readily shown that a massive spin-zero scalar free field or a massive spin-one vector free field are precluded as the dominant component of dark matter.