Formation dynamics and resulting density of long strings after percolation

Determine the formation dynamics of a percolated cosmic string network arising from growing loops of fundamental strings during a kination epoch and quantify the subsequent density of long strings, including whether and how the network enters a scaling regime after percolation.

Background

Under the condition 2H + \dot{\mu}/\mu < 0 during kination, fundamental string loops can grow faster than the scale factor and percolate to form a network. The authors argue that such a network would be expected to enter a scaling regime and survive to the present day with a tension set by the final vacuum (e.g., G\mu \sim 10^{-10} for Large Volume Scenario vacua).

However, the paper does not provide a detailed study of the percolation process, the network formation dynamics, or the resulting abundance of long strings, explicitly deferring this analysis.