The branch process of the cosmic strings

TL;DR

This paper investigates the topological structure and quantization of cosmic string defects, focusing on branch processes like generation, annihilation, and bifurcation using advanced mathematical methods.

Contribution

It introduces a detailed analysis of defect branch processes in cosmic strings using $$-mapping and topological tensor current theory, especially at critical points.

Findings

Identification of conditions for defect generation and annihilation.

Detailed description of bifurcation processes of defects.

Mathematical framework for topological quantization of cosmic strings.

Abstract

In the light of $\phi$-mapping method and the topological tensor current theory, the topological structure and the topological quantization of topological defects are obtained under the condition that Jacobian $J(\phi/v)\neq0$. When $J(\phi/v)=0$, it is shown that there exists the crucial case of branch process. Based on the implicit function theorem and the Taylor expansion, the generation, annihilation and bifurcation of the linear defects are detailed in the neighborhoods of the limit points and bifurcation points of $\phi$-mapping, respectively.