Ys. Duan et al., THE ORIGIN AND BIFURCATION OF THE SPACE-TIME DEFECTS IN THE EARLY UNIVERSE, General relativity and gravitation, 29(6), 1997, pp. 715-725
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.