As a consequence of the global definition for the cosmological constant Λ, the empirical relation Λ 2.7κρ0 (with ρ0 the density of all matter and radiation) implies that a stringent condition must be satisfied by the Lagrangian for the non-baryonic (dominant) component of dark matter. It is shown that this stringent condition is satisfied by a complex-scalar-field Lagrangian with Higgs-type quartic nonlinearity. An exact spatially homogenous solution to the associated nonlinear field equation satisfies the relation Λ 2.7κρ0 by having an amplitude and an oscillation frequency of the magnitude m 2.47×10−3 eV. Interestingly enough, the latter cosmological value for m falls in the range of the neutrino masses, suggesting that the complex-scalar cosmological field may interact with neutrinos and possibly impart mass to them via Yukawa couplings.