This paper reviews how gravitational waves from a sudden change in the early Universe — a “first‑order” phase transition — could tell us about physics beyond the Standard Model. The author summarizes a recent analysis by the LISA Cosmology Working Group and a seminar given at the Higgs pairs workshop 2025. The main conclusion is cautious: such gravitational waves can be a useful probe, but turning a detected signal into a clear identification of new particle physics is hard because different physical scenarios can give very similar signals.

Gravitational waves are tiny ripples in space that travel freely through the Universe. They decouple, or stop interacting, at very high energies, so a burst produced in the very early Universe acts like a fossil. If a phase transition in the early hot plasma was first order — meaning it proceeded by bubbles of the new phase expanding and colliding — that process can generate a stochastic gravitational wave background. Because the signal on the sky is made by many independent regions, detectors do not see single events but a random background described by a spectrum of energy versus frequency. This spectrum typically peaks at a frequency set by the size and duration of the source, which in turn maps to the temperature of the Universe when the transition happened.

The review gives concrete links between detector bands and energy scales. Ground‑based interferometers now operating (LIGO, Virgo, KAGRA) are sensitive in the roughly 1–1000 Hz band and would correspond, for sources with causal size near the Hubble length, to temperatures around 10^6–10^10 GeV. Planned third‑generation Earth instruments (Einstein Telescope and Cosmic Explorer) should be far more sensitive and could probe signals tied to the Peccei‑Quinn phase transition of axion models. The space mission LISA, planned around 2035 as a triangle of spacecraft with 2.5 million km arms, will target 10^−5–0.1 Hz and so is well matched to the electroweak energy range (roughly 10–10^5 GeV). Pulsar timing arrays, which recently found a common red noise consistent with the expected angular correlation for gravitational waves (the Hellings‑Downs curve) at 3–4.5σ, probe still lower frequencies and thus temperatures around 10 MeV–1 GeV, relevant to the QCD epoch.