content_image/336650.jpg content_image/336649.jpg content_image/336647.jpg
where Φ$_{f}$ and Φ$_{w}$ are the 24 representation of SU (5) group. The breaking component is 

where the subscript i = f, w. From (11) − (12) we obtain 

<img src='content_image/336650.jpg'>

<img src='content_image/336649.jpg'>

| σ$_{w}$ | = | σ$_{f}$ | because of the symmetry of s − matter and f − matter . Both σ$_{i}$ and m ( ϕ$_{i}$ ) are functions of temperature T . When T ≥ T$_{cr}$, σ$_{i}$ = m ( ϕ$_{i}$ ) = 0. Consequently f − particles and w − particles can easily transform from one to another so that ρ$_{F}$ = ρ$_{W}$ . When T ∼ 0 , both | σ$_{i}$ | and m ( ϕ$_{i}$ ) are large enough. Consequently interaction between f − particles and w − particles by the scalar bosons may be ignored. Thus there is only the gravitation between f − matter and w − matter when temperature is low . 

There are the couplings of fermions (and gauge particles) and scalar bosons $^{[7]}$. Hence there are the interactions of f − fermions and w − fermions shown in figures 1-3 and the interactions of f − gauge bosons and w − gauge bosons via the scalar bosons ϕ$_{f}$ and ϕ$_{w}$. In the figures the dotted lines with arrows denote W − fermion field ψ$_{w}$ , the dotted lines without arrow denote W − scalar field ϕ$_{w}$, the lines with arrows denote F − fermion field ψ$_{f}$ , the lines without arrow denote F − scalar field ϕ$_{f}$, M 2 = − 2 Aσ$_{f}$σ$_{w}$ , R$_{f}$ = − Aσ$_{f}$ , R$_{w}$ = − Aσ$_{w}$ and S = − A/ 2 . 

It can be seen from figure 1 and (13) that when − Aσ$_{f}$σ$_{w}$ > 0 and k 2 − m 2 < 0 or − Aσ$_{f}$σ$_{w}$ < 0 and k 2 − m 2 > 0 , f − fermions and w − fermions are repulsive each other; when − Aσ$_{f}$σ$_{w}$ > 0 and k 2 − m 2 > 0 or − Aσ$_{f}$σ$_{w}$ < 0 and k 2 − m 2 < 0 , f − fermions and w − fermions are attractive each other. 

## V. FEATURES AND OBSERVATION OF DARK MATTER IN PRESENT MODEL 

According to the present model [3 , $^{4]}$, v − UF M and v − UW M cannot form cluster, loosely distribute in space and have positive gravitational masses, hence both should be identified as cold dark matter. From (10) we have 

<img src='content_image/336647.jpg'>

