  In present paper the gravitational effect of spontaneous symmetry breaking
vacuum energy density is investigated by subtracting the flat space-time
contribution from the energy in the curved space-time. We found that the remain
effective energy-momentum tensor is too small to cause the acceleration of the
universe although it satisfies the characteristic of the dark energy. However
it could provide a promising explanation to the puzzle why the gravitational
effect produced by the huge symmetry breaking vacuum energy in the electroweak
theory has not been observed, since it has a sufficient small value (smaller
than the observed cosmic energy density by a factor $10^{32}$).
