The Research Of DBI Topological Defects

From the theory of phase transition at high tempreture, topological defects could be formed in the early universe during phase transition. According to their respective dimensions, they can be divided into domain wall, cosmic string, monopole and texture. Particularly, by the word "global topological defect", we mean those topological defects of which the Langrangian density does not change under global transformation. On the other hand, in the theory of brane inflation, cosmic strings could be formed due to the attraction between D-branes, while the transverse motion of D-branes is described by DBI action. Thus, it makes sense to generalize the canonical action to DBI form.In this thesis, we established DBI global cosmic strings and monopoles respectively by their dimensions, and numerically analyzed their gravitational effects. For DBI global cosmic sting, we calculated their mass of unit length by linear approximation, finding that in the region far away from the core of the string, its mass of unit length is similar with that of a canonical global string with larger core radius. Meanwhile, by analyzing the motion of test particles around the DBI global cosmic string, it shows that when the aiming distance is much larger than the core radius, it is very difficult to distinguish a DBI global cosmic string from a canonical one. However, when aiming distance is close to the core radius, there will be significant difference between them.For DBI global monopole, we asymptotically expanded the metric and calculated its core radius by formal solutions of spherical metric. We found that when the wrap factor is small enough, its effective mass is independent of the height of the potential, while in the case of a large wrap factor, the situation will reduce to that of a canonical monopole. Meanwhile, the calculation of its asymptotical mass shows the similar conclusion: when the wrap factor is very small, the asymptotical mass of DBI global monopole is independent of the height of the potential, while for large wrap factor, it reduces to a canonical monopole, i.e. the effective is dependant to the height of its potential.