Tackling tangledness of cosmic strings by knot polynomial topological invariants

TL;DR

This paper introduces a novel topological invariant based on knot polynomials, specifically the Kauffman bracket, to analyze and characterize tangled cosmic strings, offering a stronger tool than traditional linking numbers.

Contribution

It develops a new mathematical framework linking knot polynomial invariants to the topological charge of cosmic strings, enhancing the analysis of their tangled structures.

Findings

Kauffman bracket polynomial serves as a robust topological invariant for cosmic strings.

A new breaking-reconnection method models physical reconnection processes.

Topological charge derived from Hopf mapping relates to knot invariants.

Abstract

Cosmic strings in the early universe have received revived interest in recent years. In this paper we derive these structures as topological defects from singular distributions of the quintessence field of dark energy. Our emphasis is placed on the topological charge of tangled cosmic strings, which originates from the Hopf mapping and is a Chern-Simons action possessing strong inherent tie to knot topology. It is shown that the Kauffman bracket knot polynomial can be constructed in terms of this charge for un-oriented knotted strings, serving as a topological invariant much stronger than the traditional Gauss linking numbers in characterizing string topology. Especially, we introduce a mathematical approach of breaking-reconnection which provides a promising candidate for studying physical reconnection processes within the complexity-reducing cascades of tangled cosmic strings.