THE ORIGIN AND BIFURCATION OF THE SPACE-TIME DEFECTS IN THE EARLY UNIVERSE

In the early universe, a new topological invariant is interpreted as t he space-time dislocation flux and is quantized in the topological lev el. By extending to a topological current of dislocations, the dynamic form of the defects is obtained under the condition that the Jacobian determinant D(phi/u)not equal 0. When D(phi/u)=0, it is shown that th ere exists the crucial case of branch process. Based on the implicit f unction theorem and the Taylor expansion, the origin and bifurcation o f the space-time dislocations are detailed in the neighborhoods of the limit points and bifurcation points of phi-mapping, respectively. It is pointed out that, since the dislocation current is identically cons erved, the total topological quantum numbers of the branched dislocati on fluxes will remain constant during their origin and bifurcation pro cesses, which are important in the early universe because of spontaneo us symmetry breaking.