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Thus, according to the present model $^{[3]}$, there are three sorts of dark matter which are v − UF M, v − W BM and v − UW M. Given v − F BM can cluster and form visible galaxies. v − W BM can cluster and form dark galaxies. v − UF M and v − UW M cannot cluster to form any celestial body, loosely distribute in space, and their compositions are unknown. ρ$_{vWu}$/ρ$_{vFu}$ = ρ$_{vFB}$/ρ$_{vWB}$ = 1 is invariant because of the symmetry of W − matter and F − matter . 

According to the cosmological model without singularity $^{[5]}$, there are s − matter and v − matter which are symmetric and repulsive each other. In V − breaking , v − SU (5) breaks into v − SU (3) × U (1) , v − F BM forms the visible world, v − W BM, v − UF M and v − UW M form the dark-matter world; s − SU (5) does not break, all s − particles form s − SU (5) color single states which loosely distribute in whole space and cause space to expand with an acceleration in the present stage. This is because there is no interaction similar to the given electroweak interaction among the s − SU (5) color single states $^{[5]}$. 

ρ$_{s}$/ρ$_{v}$ is changeable as space expands [5] because ρ$_{vM}$ ∝ R − $^{3}$, ρ$_{vγ}$ ∝ R − $^{4}$, and ρ$_{s}$ = ρ$_{sM}$ ∝ R − $^{3}$. Here ρ$_{vM}$ and ρ$_{vγ}$ are respectively the energy density of massive v − particles and the energy density of massless v − particles , ρ$_{s}$ is the energy density of s − SU (5) color single states. The masses of all color single states are not zero, hence ρ$_{s}$ ∝ R − $^{3}$. 

## IV. THE INTERACTION OF F-SCALAR FIELDS AND W-SCALAR FIELDS 

The Ref. [7] given the interaction of F − scalar fields and W − scalar fields 

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