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A new conjecture is proposed that there are two sorts of matter calleds-matter and v-matter which are symmetric and whose gravitational masses areopposite to each other, although both masses are positive. Therefore, there aretwo sorts of symmetry breaking called V-breaking and S-breaking. In theS-breaking, s-particles get their masses and form s-galaxies etc., whilev-fermions and v-gauge bosons are still massless and form v-SU(5) singlets.There is no interaction among the v-SU(5) color-single states exceptgravitation so that they distribute loosely in space, cannot be observed andcause space to expand with an acceleration. When temperature increases to thecritical temperature because space contracts, masses of all particles are zeroso that s-particles and v-particles transform from one to another and thegravitational mass density becomes negative. Consequently, space stop tocontract and inflation must occur. After reheating, space first expands with adeceleration and then expands with an acceleration up to now. There is nospace-time singularity. There are the critical temperature, the highesttemperature and the least scale in the universe. A formula describingdistance-redshift is obtained. A huge void is not empty, and is equivalent to ahuge concave lens. The densities of hydrogen in the huge voids must be muchless than that predicted by the conventional theory. The gravitation betweentwo galaxies with distance long enough will be less than that predicted by theconventional theory. A black hole with its mass and density big enough willtransform into a white hole. Primordial nucleosynthesis and CMB are explained.It is possible that the universe is composed of infinite cosmic islands. Theproblem of energy conservation is discussed.

Cosmological Models Without Singularity Based on RW Metric or A New Metric and their Explanation for Evolution of the Universe