Topological Field Theory And Gravitational Theory Of Cosmic Strings, Order Parameter Field Dark Energy, Modification Of Universal Gravitation

Firstly,Prof.Duan'sφ-mapping topological current theory and the U(l) gauge potential decomposition theory is studied.Using the theory,the topological defect,cosmic strings,are studied.The topological spacetime defects were created at the zero points of the complex scalar order parameter field in the early Universe.In the paper,a new Lorentz gauge invariant U(l)topological field from torsion is presented,which could creat cosmic strings.The knot-like cosmic strings and it's topological invariant,the Chern-Simons action,are also studied in the paper,a step further,this action is just the total sum of all the selflinking and linking numbers of knot family.Moreover,it is also shown that this Chern-Simons action is conserved in the branch processes(splitting,merging and intersection)during the evolution of knotlike lines.Secondly,the cylindrical symmetry gravitational theory of cosmic strings is studied.The general cylindrical symmetry solution of vacuum Einstein equations is presented.In the chapter,we analyse two models:the Abelian Higgs model and Higgs complex scale field model,and caculate the gauge matric of three kinds of cosmic strings,the superconductor cosmic strings,the gauge cosmic strings and the global cosmic strings.The cosmic strings may be one of the candidates of the dark matter.Thirdly,the complex scalar order parameter field model of dark energy is studied.From the Lagrangian of the complex scalar order parameter field, we get the energy-momentum tensor of the model,then the density and the pressure.Using cosmic dynamics equation,we find that the complex scalar order parameter field could creat negtive pressure which make the expansion of the Universe is accelerating.The complex scalar order parameter field is one of the candidates of the dark energy.Finally,using general spherical symmetry solution of Einstein equations, the Newton gravitation modification at small length scale is studied.By solving the Einstein equations,we obtain general spherical symmetry solution which do not depend on any coordinate condition.Then using low velocity approximation, we get a modified formula of Newtonian gravitational theory.The theory depend on a scale factor f(r),which could not be decided by the General Relativity.