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　unoriented　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.