Scaling solutions of wiggly cosmic strings. II. Time-varying coarse-graining scale solutions

We continue our exploration of the wiggly generalization of the velocity-dependent one scale model for cosmic strings, through the study of its allowed asymptotic scaling solutions. We extend the work of a previous paper [A. R. R. Almeida and C. J. A. P. Martins, Phys. Rev. D 104, 043524 (2021).] by considering the more comprehensive case of a time-varying coarse-graining scale for the string wiggles. The modeling of the evolution of the network therefore relies on three main mechanisms: Hubble expansion, energy transfer mechanisms (e.g., the production of loops and wiggles) and the choice of the scale at which wiggles are coarse-grained. We analyze the role of each of them on the overall behavior of the network, and thus in the allowed scaling solutions. In Minkowski space, we find that linear scaling, previously observed in numerical simulations without expansion, is not possible with a changing averaging scale. For expanding universes, we find that the three broad classes of scaling solutions-with the wiggliness disappearing, reaching scaling, or growing-still exist but are differently impacted by the time evolution of the coarse-graining scale. Nambu-Goto type solutions (without wiggles) are unaffected, growing wiggliness solutions are trivially generalized, while for solutions where wiggliness reaches scaling the expansion rate for which the solution exists is decreased with respect to the one for a fixed coarse -graining scale. Finally, we also show that the inclusion of a time-varying coarse-graining scale allows, in principle, for additional scaling solutions which, although mathematically valid, are not physical. Overall, our mapping of the landscape of the allowed scaling solutions of the wiggly velocity-dependent one scale model paves the way for the detailed testing of the model, to be done by forthcoming high-resolution field theory and Nambu-Goto simulations.

Automated summary

This study explores the allowed scaling solutions of the wiggly velocity-dependent one scale model for cosmic strings, focusing on the impact of a time-varying coarse-graining scale for the string wiggles. The results show that the behavior of the network and the existence of scaling solutions are influenced by factors such as Hubble expansion, energy transfer mechanisms, and the choice of coarse-graining scale. The inclusion of a time-varying coarse-graining scale allows for additional scaling solutions, although these solutions may not be physically meaningful.