The Evolution Of The Very Early Universe Based On Duan's Topological Current Theory And The Open String Theory With The Antisymmetric Background Field

In this thesis, using the gauge potential decomposition theory and theφ-mapping topological current theory which were originally proposed by Prof.Duan, we have studied in detail the topological properties of the cosmic strings,the relationship between the spin of the cosmic strings and the torsion of theextra dimensional spaces, the roles of the cosmic strings and the inflation inthe very early evolution of the universe, the evolution picture of the very earlyuniverse in cosmology, and the topological properties of the anyons in planarphysics. Also we have studied the relationship between the boundary conditionsof the bosonic open string and the open superstring and the noncommutativityof the spacetime coordinates in string theory.Firstly, through the analysis of the formation mechanism and topologicalproperties of the cosmic strings, we have showed that, the cosmic stringsare formed after the automatically symmetric broken phase transition of thecomplex scalar Higgs field in the very early history of the universe, their topologicalstructures, topological charges etc. can all be described in terms of theHiggs field which had reached its expectation values. Combining with the 4-dimensional spacetime effective theory when there exist extra dimensions, wehave studied that the torsion of the extra dimensional space can be described bya U(1) gauge potential, and this gauge potential would get coupled to the Higgsfield and get trapped into the cosmic strings when the cosmic strings form, andthen it would act as some kind of source of the spins of the cosmic strings.Meanwhile, we have discussed that before the phase transition the symmetryof the Higgs field is global, and the field could act as the inflaton to derive theuniverse space to inflate. Then combining the whole discussion of the cosmicstrings, the torsion and the inflation, we have constructed a brief evolution pictureof the very early universe. Secondly, as a simple application of the topological current theory, wehave studied some topological properties of the anyons in planar physics. I haveshowed that, the basic charge of the anyons actually has structures, namely it istotally decided by the two coupling constants of the system; also the phase factorof the Aharonov-Bohm type interactions among the anyons is proportionalto the Chern-Simons coupling constant.Also we have studied the relationship of the open string and the spacetimestructure in string theory, we have discussed that, when there exists an antisym-metric2-order background field besides the metric field, the original Neumannand Dirichlet boundary conditions of the open string would mix; and as a result,for bosonic open string, the spacetime coordinates of its endpoints become noncommutative,in the directions both parallel and perpendicular to the D-branes,and for open superstring, the whole phase space, namely the space of coordinatesand momentum, of the string endpoints becomes noncommutative.