THE QUANTIZATION AND PRODUCTION OF THE SPACE–TIME DEFECTS IN THE EARLY UNIVERSE

Abstract

In Riemann–Cartan manifold U4, a new topological invariant is obtained by means of the torsion tensor. In order to describe the space–time defects (which appear in the early universe due to torsion) in an invariant form, the new topological invariant is introduced to measure the size of defects and it is interpreted as the dislocation flux in internal space. By the use of the so-called ϕ mapping method and the gauge potential decomposition, the dislocation flux is quantized in units of the Planck length. The quantum numbers are determined by the Hopf indices and the Brouwer degrees. Furthermore, the dynamic form of the dislocations is studied by defining an identically conserved current. Based on the implicit function theorem, the production of the defects at the limit points is detailed.