Formation of topological and nontopological defects in the early universe

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The formation of defects in the early universe is investigated used the Kibble mechanism. The distinction between topological and nontopological defects is discussed. the probability for formation of a topological defect in a d-dimensional physical space is found to be 1 2 d . The probability for formation of nontopological configurations with given winding number n is obtained and their evolution is discussed. A simple criterion for a configuration to be regarded as a defect is given for the nontopological texture. We find the critical winding above which a texture forms to be in the interval n c ϵ [ 1 2 , 1] , which leads to a probability for formation per correlation volume in the range from 0.01 to 0.21.