A bstract We study string formation and dynamics in a scalar field theory with a global U(1) symmetry. If a scalar field Φ subject to a wine-bottle potential is initially displaced from the potential minimum, and even if this is done uniformly and coherently over large spatial patches, we show that small spatial perturbations to Φ grow through parametric resonance as Φ oscillates; this observation holds over a wide range of initial U(1) charge densities. We show that the growth of these perturbations leads to the formation of spatially coherent, temporally stable counter-rotating regions ; i.e., spatially connected regions that exhibit Φ evolution with large and opposite-sign rotation speeds in field space and that persist over long durations. These counter-rotating regions are separated by domain boundaries characterized by a large field gradient and zero rotational speed in field space. We find that string or vortex topological defects form, are confined to, and then annihilate periodically on these domain boundaries. We demonstrate these periodic dynamics with numerical simulations in both 2 + 1 and 3 + 1 dimensions, in both Minkowski spacetime and in a radiation-dominated Friedmann-Lemaître-Robertson-Walker (FLRW) universe, and we explain some features of the evolution (semi-)analytically. At late times in an expanding universe, when Φ approaches the minimum of the potential, we find counter-rotating regions and vortices to dissipate into scalar radiation. Phenomenologically, periodic bursts of string formation and annihilation are expected to lead to periodic bursts of gravitational-wave production. For small initial U(1) charge density, these gravitational-wave bursts can be synchronized across the whole Universe. Owing to their periodic nature, it is possible that they could give rise to a gravitational-wave frequency spectrum consisting of a forest of fully or partially resolved peaks. We find that these periodic scalar field dynamics also occur with large (but not fine-tuned) initial U(1) charge density; they may thus have implications for models that depend on a coherent field rotation, such as kination and the axion kinetic-misalignment mechanism.
Fedderke et al. (Tue,) studied this question.