Gravitational Waves from Phase Transitions

Abstract

We summarise the physics of first-order phase transitions in the early universe, and the possible ways in which they might come about. We then focus on gravitational waves, emphasising general qualitative features of stochastic backgrounds produced by early universe phase transitions and the cosmology of their present-day appearance. Finally, we conclude by discussing some of the ways in which a stochastic background might be detected.

Figures (10)

• Figure 1: Fog and sea ice in the Arctic Ocean. As water vapour -- the gaseous phase of water -- cools, it condenses to form clouds of liquid water such as the fog seen here. Water, when it cools still further, freezes to form ice. The condensation and freezing of water are two everyday examples of first order phase transitions.
• Figure 2: Chronology of the very early universe. The key events discussed in Section \ref{['sec:early']} are shown, along a logarithmic timeline. The relationship between time and temperature shown here assumes that the energy density of radiation dominates the universe's expansion, and that there are no additional degrees of freedom beyond those known about in the Standard Model of particle physics. Various events in the history of the universe could have produced gravitational waves, see Table \ref{['tab:GWEvents']}.
• Figure 3: Symmetry breaking potential of the Abelian Higgs model, resembling the underside of a wine bottle. Left: Though the potential is symmetric, the vacuum (indicated in red) is not at $|\Phi| = 0$, indicating spontaneous symmetry breaking has taken place. Right: Cross section of the potential at various temperatures: at high temperature (red line), the lowest energy state is symmetric about the zero axis. At low temperature (blue lines) the lowest energy states are not symmetric, even though the potential energy curve is.
• Figure 4: Form of the potential \ref{['eq:firstorderpotential']} at an intermediate temperature $m<T<2 m \sqrt{\lambda}/\sqrt{4\lambda-1}$.
• Figure 5: Best-case scenarios for gravitational wave power spectra, in the cases given in Table \ref{['tab:GWEvents']}. Note that setting $C=0.1$ is a simplistic approach to computing the anticipated amplitude of the different scenarios, but that otherwise there is a very mild dependence on the number of relativistic degrees of freedom. Also shown are the power-law integrated sensitivity curves Thrane:2013oya anticipated for advanced LIGO and for LISA Babak:2021mhe, each assuming a 5 year observation time, and for NANOGrav NANOGrav:2023ctt based on the 15 year data release. If a background signal has a power-law shape and intersects the shaded regions, then in the absence of astrophysical foregrounds, it may be detectable. Our sensitivity curves assume a signal-to-noise ratio of 5.