THE PROBABILITY FOR FORMATION OF COLLAPSING TEXTURES AND TEXTURE KNOTS

Global textures are interesting because they are promising candidates for seeds in the structure formation of the universe. The important configurations are those which will be able to collapse. The type of configurations that I will consider are half knots and true knots. I define a half knot as one that covers more than a half-S3, and a true knot as a configuration that covers the whole of S3. Configurations that are half knots will be able to collapse, a new argument for this collapse criterion is given in this paper. I will also give some critical remarks on the method of using the total winding number as a criterion for identifying a knot. I propose another more direct method and make use of it when I estimate the probability for formation of both true and half knots by numerical simulations. In three dimensions the probability for formation of a true knot is found to be P(knot) = 0.003 and the probability for formation of a half knot is found to be P(half) = 0.066. Taking into account the chance of annihilation the probability for collapse is found to be in the interval p(coll) is-an-element-of [0.01, 0.04]. In the skyrmion picture of hadrons the investigations of formation of true knots are important, and some implications of my result on the predictions of a ''topological'' theory of baryon production in jets are discussed.