International Astronomy and Astrophysics Research Journal

We present a basic model for the formation of a stress-free universe, which shows that its formation gives rise to a wave and particle mass, which together characterize the universe. In this model a decaying exponential expansion rate is responsible for the particle mass (M_P) and a growing exponential expansion rate is responsible for the wave mass (M_W).  The evolution of the universe is governed by the ratio (α = M_P/M_W) in which α = K_o/c where K_o is the initial expansion rate and c is the velocity of light. In a stress-free expansion process, 0 ≤ α ≤ ½, the mass ratio, M_P/M_W = α. The mass of the universe, M = M_W + M_P, in which it is found from the exponential model that M_W = m_o c T/ ln (1/α) where T is the age of the universe and m_o = c²/G where G is the universal gravitational constant.  Observations of the mass and age of the universe, yield, α = 0.235, and hence M_P / M = 0.19. This ratio is very close to the ratio of ordinary matter to dark matter of 0.18 in [1].  Hence, the wave mass, M_W, can be interpreted as the dark matter remaining after the formation of the particle matter. The analysis also shows that on temporal scales (t_o) much less than the age of the universe (T), M_P (t_o) / M_W(t_o) → 1, which is an exact wave-particle duality.