Enhancing Gravitational Waves from Global Strings via a First-Order Phase Transition

We perform the first (3+1)-dimensional lattice simulations of a cosmological first-order phase transition (PT) in which true-vacuum bubbles with random phases nucleate, expand, and collide, producing a network of global strings. We find that the string network enters the scaling regime, and the coefficient of the logarithmic growth is smaller than the value obtained for a second-order PT. From the axion spectrum, we derive the dark-matter relic abundance and the dark-radiation bound from big bang nucleosynthesis on the axion decay constant fₐ and mass mₐ. The ratio of the gravitational wave emission rate to the axion emission rate is found to be about two orders of magnitude larger than in the second-order case, and the resulting gravitational wave spectrum can be probed by pulsar timing arrays as well as by space- and ground-based interferometers.