  It is widely believed that as one of the candidates for dark energy, the
cosmological constant should relate directly with the quantum vacuum. Despite
decades of theoretical effects, however, there is still no quantitative
interpretation of the observed cosmological constant. In this work, we consider
the quantum state of the whole universe including the quantum vacuum. Everett's
relative-state formulation, vacuum quantum fluctuations and the validity of
Einstein's field equation at macroscopic scales imply that our universe wave
function might be a superposition of states with different cosmological
constants. In the density matrix formulation of this quantum universe, the
quasi-thermal equilibrium state is described by a specific cosmological
constant with the maximum probability. Without any fitting parameter, the ratio
between the vacuum energy density due to the cosmological constant (dark
energy) and the critical density of the universe is 68.85% based on simple
equations in our theoretic model, which agrees very well with the best current
astronomical observations of 68.5%.
