A new insight into the negative-mass paradox of gravity and the accelerating universe

The discovery of acceleration of the universe expansion in recent astrophysics research prompts the author to propose that the Newton's gravitation law can be generalized to accommodate the antimatter: While the force between matters(antimatters) is attractive, the force between matter and antimatter is a repulsive one. A paradox of negative-mass in gravity versus a basic symmetry (m-->-m) based on quantum mechanics is discussed in sufficient detail so that the new postulate could be established quite naturally. Corresponding modification of the theory of general relativity is also suggested. If we believe in the symmetry of particle and antiparticle as well as the antigravity between them, it might be possible to consider a new scenario of the expansion of universe which might provide some new insight into the interpretation of cosmological phenomena including the accelerating universe observed.