Gravitational waves from first-order phase transitions in the early universe

Abstract

We discuss stochastic gravitational waves sourced from cosmological first-order phase transitions. The recent development of gravitational-wave observatories opens a new era of multi-messenger astronomy, and in the upcoming decades, cosmological sources of gravitational waves would be a new passage towards high-energy phenomena. The first-order phase transition as a cosmological source is one of the interesting candidates beyond the standard model. Despite much attention to the models of first-order phase transitions, there are several logical gaps in the dynamics during the phase transition about each contribution of sources to gravitational waves, the amount of generated gravitational waves, decay processes of sources, and determination of the bubble wall speed. As a part of the efforts, we investigate analytic approaches to the power spectrum of gravitational waves and the evolution of fluid sources with parametrizing the dynamics of phase transitions. We especially focus on the very strong first-order phase transitions because the extremeness would result in strong signals, and in addition, it is rarely investigated on account of the hardness of the problem. We investigate two independent aspects of strong first-order phase transitions, bubble nucleation rate and fluid shocks as gravitational-wave sources. First, since the approximated exponential form of the bubble nucleation rate would not be valid in the strong phase transition regime, we consider the next-order correction to the rate and see the implications for the gravitational wave power spectrum. The correction appears through the sharpness of the normalized power spectrum, and future sensitive observatories are expected to distinguish the difference. Second, if the speed of the scalar bubbles gets to the terminal velocity by friction which is originated from microphysical processes, then the bulk motion of radiation which is called fluid bubble would be the dominant source of gravitational waves. In the very strong first-order phase transition regime, we study the early phase of the fluid bubbles. Since the fluid bubbles form shock waves, through understanding the dynamics of shocks, we find how the shocks decay through nonlinear propagation and the consequences for gravitational waves. Although many debates are ongoing, and there remain questions still, but the analytic approaches will certainly deepen our understanding of gravitational waves from cosmological first-order phase transitions.