Scaling solution for cosmological models at large N

We study the evolution of the nonlinear O(N) model in an expanding universe in the large-N approximation, where one can solve exactly for the scaling field distribution, incorporating the full nonlinear dynamics. This provides a valuable analytic approximation for theories of cosmic global monopoles (N=3), global texture (N=4), and "nontopological texture" (N>4). The analytic results are compared with those from numerical simulations, with good agreement. The probability distribution for mass fluctuations in the linear regime is positively skewed, providing a distinctive test for the theory.