Knotlike Cosmic Strings in The Early Universe

TL;DR

This paper explores the topological properties of knotlike cosmic strings in the early universe's Riemann-Cartan space-time, introducing a new invariant based on Chern-Simons theory that remains conserved during string evolution.

Contribution

It introduces a topological invariant for knotlike cosmic strings derived from Chern-Simons theory, linking it to self-linking and linking numbers, and shows its conservation during cosmic string evolution.

Findings

A topological invariant for knotlike cosmic strings is constructed.

The invariant equals the sum of self-linking and linking numbers.

The invariant is conserved during cosmic string branch processes.

Abstract

In this paper, the knotlike cosmic strings in the Riemann-Cartan space-time of the early universe are discussed. It has been revealed that the cosmic strings can just originate from the zero points of the complex scalar quintessence field. In these strings we mainly study the knotlike configurations. Based on the integral of Chern-Simons 3-form a topological invariant for knotlike cosmic strings is constructed, and it is shown that this invariant is just the total sum of all the self-linking and linking numbers of the knots family. Furthermore, it is also pointed out that this invariant is preserved in the branch processes during the evolution of cosmic strings.