Spinodal Gravitational Waves

TL;DR

This work identifies and quantifies a spinodal mechanism for gravitational-wave production during cosmological first-order thermal phase transitions, active when bubble nucleation is strongly suppressed. Using a holographic Einstein-scalar model, the authors map real-time gauge theory dynamics to 5D gravity and compute the resulting GW spectrum arising from spinodal growth of unstable modes and subsequent phase-domain merging. They show that the GW signal from spinodal dynamics is qualitatively distinct from bubble-nucleation scenarios, with an early exponential growth of modes below a cutoff at k ≈ 2 k_max and a substantial portion of energy emitted during a short nonlinear reshaping phase; the spectrum and its evolution depend on whether the transition occurs in the sector driving expansion or in a hidden sector and on the thermodynamic path (including potential thermal inflation). The study provides a first principled calculation of spinodal GW production in a strongly coupled gauge theory, offering a framework to extend to expanding backgrounds and backreaction and informing prospects for future GW observations from high- or low-frequency regimes.

Abstract

We uncover a new gravitational-wave production mechanism in cosmological, first-order, thermal phase transitions. These are usually assumed to proceed via the nucleation of bubbles of the stable phase inside the metastable phase. However, if the nucleation rate is sufficiently suppressed, then the Universe may supercool all the way down the metastable branch and enter the spinodal region. In this case the transition proceeds via the exponential growth of unstable modes and the subsequent formation, merging and relaxation of phase domains. We use holography to follow the real-time evolution of this process in a strongly coupled, four-dimensional gauge theory. The resulting gravitational wave spectrum differs qualitatively from that in transitions mediated by bubble nucleation. We discuss the possibility that the spinodal dynamics may be preceded by a period of thermal inflation.

Figures (19)

• Figure 1: Free energy density (top) and energy density (bottom) of the four-dimensional gauge theory dual to (\ref{['action']})-(\ref{['param']}). States on the solid, blue curves are thermodynamically stable. States on the dashed, brown curves are metastable. States on the dashed-dotted, red curve are unstable. The black circle with $T=0.3908\Lambda$ indicates the initial state on which we will focus in this paper.
• Figure 2: Speed of sound squared (top) and ratio of the bulk viscosity over the shear viscosity (bottom) versus temperature for the gauge theory dual to (\ref{['action']})-(\ref{['param']}). The color coding is as in Fig. \ref{['free']}. The dotted, green curve in the top figure corresponds to the approximation (\ref{['csclose']}).
• Figure 3: Hydrodynamic approximation to the growth rates $\gamma(k)$ for different states on the spinodal region of Fig. \ref{['free']}.
• Figure 4: Comparison between the hydrodynamic values of $k_*$ (top) and $\gamma_\textrm{max}$ (bottom) given by (\ref{['small']}) (solid curves) and the ball-park estimates (\ref{['ball']}) (dashed curves).
• Figure 5: Energy density plus three times the pressure for the four-dimensional gauge theory dual to (\ref{['action']})-(\ref{['superpotential']}) with the choice of parameters (\ref{['param']}).