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Cosmic strings in the early universe have received revived interest in recentyears. In this paper we derive these structures as topological defects fromsingular distributions of the quintessence field of dark energy. Our emphasisis placed on the topological charge of tangled cosmic strings, which originatesfrom the Hopf mapping and is a Chern-Simons action possessing strong inherenttie to knot topology. It is shown that the Kauffman bracket knot polynomial canbe constructed in terms of this charge for un-oriented knotted strings, servingas a topological invariant much stronger than the traditional Gauss linkingnumbers in characterizing string topology. Especially, we introduce amathematical approach of breaking-reconnection which provides a promisingcandidate for studying physical reconnection processes within thecomplexity-reducing cascades of tangled cosmic strings.

Tackling tangledness of cosmic strings by knot polynomial topological invariants