Global texture as the origin of large-scale structure: Numerical simulations of evolution

Numerical simulations explore the evolution of global texture in an expanding universe. The evolution is surprisingly simple—"knots," regions with a nonzero winding number, collapse and unwind at a fixed rate per horizon volume per horizon time; the comoving density of knots $n$ unwinding in a conformal time interval $d\eta$ obeys $\frac{\mathrm{dn}}{d\eta }\simeq 0.04{\eta }^{-4\mathrm{}}$. During each collapse, asymmetries are damped and the texture knots appear to approach an exact spherically symmetric scaling solution. The locations of the knots are anticorrelated on scales smaller than the horizon scale and uncorrelated on larger scales. We calculate the density and pressure in the texture "scaling solution" in the matter and radiation eras. We estimate (in a universe dominated by cold dark matter with $\Omega =1\mathrm{}$) that of order ten knots of angular radius of order 8° should be visible on the microwave sky.