Effect of high harmonic loops on gravitational wave bounds from cosmic strings

Based on a binary tree model for the self-intersection of cosmic string loops containing high harmonics we estimate the number of self-intersections of the parent and daughter loops and the associated cusp production to determine the most likely number of cusp events per period on the resultant non-self-intersecting loops, and provide an updated calculation for the gravitational wave signal that arrives on Earth from cusps on such loops. This is done for different numbers of cusps supported from the cosmic strings of the network, and for different harmonic distributions on the loops. We plot our results of the event rate of gravitational waves emanating from the cusps in terms of redshift, having fixed the value of G mu and the received frequency of the signal, and compare our results to those in [B. P. Abbott et al., Constraints on cosmic strings using data from the first Advanced LIGO observing run, Phys. Rev. D 97, 102002 (2018); R. Abbott et al., Constraints on Cosmic Strings Using Data from the Third Advanced LIGO-Virgo Observing Run, Phys. Rev. Lett. 126, 241102 (2021)].