Density of strings formed at a second-order cosmological phase transition

Abstract

We discuss the problem of estimating the characteristic length scale $ξ_{\rm s}$, and hence the initial density, of a system of cosmic strings formed at a continuous, second-order phase transition in the early universe. In particular, we examine the roles of the correlation length (or string width) $ξ_{\rm c}$ and the Ginzburg length $ξ_{\rm G}$ which defines the ``fuzziness'' of long strings. We argue that strings acquire a clear identity only once $ξ_{\rm s}$ exceeds both $ξ_{\rm c}$ and $ξ_{\rm G}$, and estimate its magnitude at that time.