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

TL;DR

This paper estimates the initial density and characteristic length scale of cosmic strings formed during a second-order phase transition in the early universe, considering the roles of correlation length and Ginzburg length.

Contribution

It introduces a framework for understanding when cosmic strings become well-defined, based on the relation between characteristic length scales and phase transition parameters.

Findings

Strings acquire a clear identity when _s exceeds both _c and _G

Estimates the magnitude of _s at the time strings become well-defined

Highlights the importance of correlation and Ginzburg lengths in string formation

Abstract

We discuss the problem of estimating the characteristic length scale $\xi_{\rm s}$, 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) $\xi_{\rm c}$ and the Ginzburg length $\xi_{\rm G}$ which defines the ``fuzziness'' of long strings. We argue that strings acquire a clear identity only once $\xi_{\rm s}$ exceeds both $\xi_{\rm c}$ and $\xi_{\rm G}$, and estimate its magnitude at that time.