Texture collapse

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Abstract
We study single-texture collapse using a leapfrog discretization method on a 30×30×30 spatial lattice. We investigate the influence of boundary conditions, physical size of the lattice, type of space-time background (flat, i.e., nonexpanding, vs radiation-dominated and matter-dominated universes), and spatial distribution of the initial texture configuration on collapse time and critical winding. For a spherically symmetric initial configuration of size equal to the horizon size on a lattice containing 12 (30) horizon volumes, the critical winding is found to be 0.621±0.001 (0.602±0.003) (flat case), 0.624±0.002 (0.604±0.005) (radiation era), 0.628±0.002 (0.612±0.003) (matter era). The larger the physical size of the lattice (in units of the horizon size), the smaller is the critical winding, and in the limit of an infinite lattice, we argue that the critical winding approaches 0.5. For radially asymmetric cases, contraction of one axis (pancake case) slightly reduces collapse time and critical winding, and contraction of two axes (cigar case) reduces collapse time and critical winding significantly.

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