The present work investigates the nature of the vacuum energy density within the context of the Higgs theory. Current theories describe the empty universe in terms of the stress-energy tensor of a perfect fluid and estimate the vacuum energy density in terms of the zero-point energy of the vacuum fluctuations. In the view of the Higgs theory, empty space is a very strongly correlated quantum condensate with spontaneously broken U(1) symmetry, ruled by an Order Parameter and giving mass to the elementary particles by the Higgs mechanism. Its large energy gap (~200 GeV) strongly suppresses vacuum fluctuations and the zero-point energy. Therefore, estimating the vacuum energy density, in terms of the zero-point energy, certainly is inadequate. The Higgs universe is an adiabatic system whose total energy must be conserved. Contrarily than assumed in particle physics, expansion of the universe (Higgs Quantum Space) does not create energy. It only reduces the energy density. It stretches the wave-length of particles and of radiation, thereby reducing the energy and temperature of the matter universe. The present work shows that this adiabatic expansion leads to a vacuum energy density in close agreement with the actual observations. However, these observations in addition clearly indicate that the accelerating expansion of the visible universe keeps to the accelerating expansion of the HQS itself.