Gravitational waves from cosmic strings with friction: analytical approximations and parameter space

We derive analytical approximations to describe the ultra-high-frequency secondary peak of the stochastic gravitational wave background generated by cosmic strings that is sourced by loops created in the friction-dominated era. We show that these approximations provide a very good description of the contribution of the friction-era loops over the relevant frequency range and for a broad range of cosmic string parameters, thus enabling a fast and accurate characterization of this signature. We also use these approximations to uncover the full parameter range in which this ultra-high-frequency peak should be distinguishable on the stochastic gravitational wave background spectrum and show that it should be present in a broader range of high-energy physics scenarios than originally reported in~\cite{Mukovnikov:2024zed}.