An Accelerated Expansion Model in the Absence of the Cosmological   Constant
  Based on some observations, the apparent energy, associated with gravity, of vacuums is defined, with that of normal vacuums to be zero and that of the vacuums losing some energy to be negative. An important application of the energy is its contribution to Einstein's equation. A cosmological model, accounting for recent observations of the accelerated expansion of the universe, in the absence of the cosmological constant, can be well constructed. In a certain case, the expansion of the universe would be decelerated at its early epoch and accelerated at its late epoch. The curvature of the universe would depend on the ratio of matter energy to total energy. The missing mass problem does no longer exist in this model. Most negative apparent energy vacuums might be contained in voids, then the spacetime of galaxy clusters or that of the solar system would not be significantly affected by this kind of energy. 
Yi-Ping Qin