--- title: "What a bubbling early universe would leave in gravitational waves" description: "If the hot early universe changed state through bubbles, their sound would leave a faint hum of gravitational waves near a millihertz today." canonical_url: "https://sandboxphysics.com/stories/phase-transition-gravitational-waves/what-a-bubbling-early-universe-leaves-in-gravitational-waves/" language: "en" page_type: "story" alternate_languages: zh-CN: "https://sandboxphysics.com/zh/stories/phase-transition-gravitational-waves/what-a-bubbling-early-universe-leaves-in-gravitational-waves/" last_modified: "2026-11-12" --- [Phase-transition gravitational waves](https://sandboxphysics.com/stories/phase-transition-gravitational-waves/) # What a bubbling early universe would leave in gravitational waves Sandbox Physics · 2026-11-12 If the early universe changed state the way supercooled water freezes, with bubbles of the new state appearing and merging, it would have set the hot plasma ringing like a struck bell. That ringing shakes space itself. Stretched by fourteen billion years of expansion, it would reach us today as a faint hum of gravitational waves at about a thousandth of a hertz, the band the planned LISA observatory is built to hear. ## Before you begin No physics beyond school is needed. It helps to know that sound is a pressure wave and that the universe has been expanding since it was hot and dense. ## Water that stays liquid below freezing Very clean water can be cooled a few degrees below zero and stay liquid. When it finally freezes, ice does not appear everywhere at once. Small crystals form at scattered points, grow and run into each other until no liquid is left. Physicists call a change of state like this a first-order phase transition. Many particle-physics models beyond the Standard Model predict that the young universe went through one, a tiny fraction of a second after the Big Bang, when the temperature was around a hundred to a thousand times the energy of a proton at rest. In those models the new state appears as bubbles that expand into the old one at a large fraction of the speed of light. Nobody knows yet whether this happened. That is why a signal from it would be worth looking for: it would tell us about physics at energies no collider reaches directly. Reading: Caprini et al., Gravitational waves from first-order phase transitions in LISA: reconstruction pipeline and physics interpretation, arXiv:2403.03723v2 / JCAP 10 (2024) 020 · Caprini et al., Detecting gravitational waves from cosmological phase transitions with LISA: an update, arXiv:1910.13125v2 / JCAP (2020), doi:10.1088/1475-7516/2020/03/024 ## The bubbles set the plasma ringing The early universe was filled with a hot soup of particles, a plasma. As a bubble wall sweeps through it, the wall releases energy and pushes the plasma, the way a boat pushes a bow wave. Each bubble drags a thin shell of moving plasma along with it. When bubbles meet and merge, the walls disappear but the moving shells keep going. They travel on as sound waves and cross each other many times. Sound means plasma squeezed in some places and thinned in others, and moving, squeezed matter changes how space is stretched around it. A changing pattern like that sends out gravitational waves, ripples in the shape of space itself. In the models where the walls feel strong friction from the plasma, this sound is the loudest source. The bubbles colliding matter less than the long ringing that follows them. Reading: Caprini et al., Gravitational waves from first-order phase transitions in LISA: reconstruction pipeline and physics interpretation, arXiv:2403.03723v2 / JCAP 10 (2024) 020 · Espinosa, Konstandin, No & Servant, Energy budget of cosmological first-order phase transitions, arXiv:1004.4187v1 / JCAP 1006:028 (2010) ## Why the hum is near a millihertz today The pitch of the hum is set by the size of the bubbles when they merged. In a fast transition, many bubbles appear and each stays small, a few percent of the distance light could travel in the age of the universe at that time. Smaller bubbles ring at a higher pitch. Then the universe expanded, and every wave was stretched with it. For a transition at a temperature of 200 billion electronvolts, distances have grown about two and a half million billion times since then. A wave that once fitted inside a bubble now takes many minutes to pass. In our worked example the spectrum peaks near 0.68 millihertz, a period of about 25 minutes. The strength also changes. The energy in gravitational waves is diluted as the universe expands. In our example the signal today carries a few parts in a hundred billion of the energy density that makes the universe flat. That is still within reach of an instrument with arms millions of kilometres long. Reading: Caprini et al., Gravitational waves from first-order phase transitions in LISA: reconstruction pipeline and physics interpretation, arXiv:2403.03723v2 / JCAP 10 (2024) 020 · Original benchmark tutorial materials (standard-library Python) ## What LISA could learn from the shape LISA is a planned gravitational-wave observatory: three spacecraft in a triangle with sides of 2.5 million kilometres, timing laser light between free-falling test masses. The European Space Agency has adopted the mission, with launch planned in the 2030s. Its best sensitivity lies between about a tenth of a millihertz and a tenth of a hertz. A phase transition would not make a single tone but a broad hump. Where the hump peaks tells us how large the bubbles were, and therefore how fast they formed. How high it rises depends on how much energy reached the moving plasma and how long the sound lasted before it broke up into shocks and turbulence. There is a catch. The hump has only a few features, its height and two bends, while the transition has more unknowns: its strength, its speed, its temperature and the speed of the walls. The 2024 LISA study shows that the shape alone leaves some of these tangled together, and that adding a model of the particle physics, or a second source, can separate them. Reading: Caprini et al., Gravitational waves from first-order phase transitions in LISA: reconstruction pipeline and physics interpretation, arXiv:2403.03723v2 / JCAP 10 (2024) 020 · Robson, Cornish & Liu, The construction and use of LISA sensitivity curves, arXiv:1803.01944v2 / Class. Quantum Grav. (2019), doi:10.1088/1361-6382/ab1101 ## How sure the prediction is The spectra are built from computer simulations of bubbles and plasma, then summarised by a formula with a few numbers in it. That formula works best when the walls move clearly slower or clearly faster than sound. Close to the speed of sound, the moving shells become thin and the formula no longer describes the simulations well. For strong transitions the sound breaks into shocks within a fraction of the expansion time, so the signal is smaller than an older, simpler estimate suggested. No such background has been detected. Every number on this page is a model prediction for a chosen set of parameters, and the Lab marks the parameter settings where the formula holds. Reading: Caprini et al., Detecting gravitational waves from cosmological phase transitions with LISA: an update, arXiv:1910.13125v2 / JCAP (2020), doi:10.1088/1475-7516/2020/03/024 · Ellis, Lewicki & No, Gravitational waves from first-order cosmological phase transitions: lifetime of the sound wave source, arXiv:2003.07360v4 / JCAP 07 (2020) 050 ## Exercises and explained answers 1. Two transitions happen at the same temperature. In the first, bubbles form ten times faster than in the second. Which one gives a hum at higher frequency today? Read the explanation The faster one. Faster formation means more bubbles, each smaller when they merge. Smaller bubbles ring at shorter wavelengths, and expansion stretches both signals by the same factor because the temperature is the same. The peak frequency rises roughly in proportion to the formation rate. 2. Why does the same transition give a lower frequency today if it happened at a lower temperature? Read the explanation A transition at lower temperature happened later, when the universe was larger and the expansion rate was smaller. Bubbles were bigger in absolute terms, and the waves have been stretched by a smaller factor since then, but the first effect wins: the frequency today scales in proportion to the temperature at the transition. ## Try the prediction ### [Watch bubbles merge and leave sound rings](https://sandboxphysics.com/labs/phase-transition-gravitational-waves/) 1. Watch the default scene without touching anything. Bubbles appear, merge, and leave fading gold sound rings. 2. Pick the preset Rapid and faint and see the peak move to higher frequency and drop. [Next: How bubbles appear and fill space](https://sandboxphysics.com/stories/phase-transition-gravitational-waves/how-bubbles-appear-and-fill-space/) ## Sources and calculation scope 1. [Caprini et al., Gravitational waves from first-order phase transitions in LISA: reconstruction pipeline and physics interpretation, arXiv:2403.03723v2 / JCAP 10 (2024) 020](https://arxiv.org/abs/2403.03723v2) Read in the arXiv v2 LaTeX source: abstract and introduction, section 2.2.1 (sound-wave double broken power law, amplitude, mean bubble separation and redshift factors), section 3 and appendix A (two-parameter LISA noise and response) and the opening of section 5 on reconstruction. The noise equation prints the optical-metrology corner as 2e-3 mHz; our materials use 2 mHz and report both results. Figure 2 was read from its caption only. 2. [Caprini et al., Detecting gravitational waves from cosmological phase transitions with LISA: an update, arXiv:1910.13125v2 / JCAP (2020), doi:10.1088/1475-7516/2020/03/024](https://arxiv.org/abs/1910.13125v2) Read the LaTeX source in two places: the sound-wave signal section (signal.tex, about lines 180 to 260) and the definition of the root-mean-square fluid velocity and kinetic-energy fraction (prelim.tex, lines 171 to 182). Used for the earlier shock-time definition only. 3. [Espinosa, Konstandin, No & Servant, Energy budget of cosmological first-order phase transitions, arXiv:1004.4187v1 / JCAP 1006:028 (2010)](https://arxiv.org/abs/1004.4187v1) Read the fluid equations for a single self-similar bubble, the deflagration, hybrid and detonation profiles, and the appendix-B efficiency fits with their stated precision of better than 15 percent. Our own profile solutions in the bag model check the fits independently. 4. [Ellis, Lewicki & No, Gravitational waves from first-order cosmological phase transitions: lifetime of the sound wave source, arXiv:2003.07360v4 / JCAP 07 (2020) 050](https://arxiv.org/abs/2003.07360v4) Read the LaTeX source for the shock-formation time, the mean fluid velocity written through the efficiency, and the argument that the sound-wave source switches off well before a Hubble time for strong transitions. 5. [Robson, Cornish & Liu, The construction and use of LISA sensitivity curves, arXiv:1803.01944v2 / Class. Quantum Grav. (2019), doi:10.1088/1361-6382/ab1101](https://arxiv.org/abs/1803.01944v2) Located the optical-metrology and test-mass noise terms and the sensitivity formula in the LaTeX source. Used only as an independent check of the noise curve shape and of the 2 mHz corner; the paper was not read section by section. 6. [Original benchmark tutorial materials (standard-library Python)](https://sandboxphysics.com/stories/phase-transition-gravitational-waves/materials/README.md) Our script, three fixed benchmarks, four failure cases and the expected output. It evaluates the published parametric template, the efficiency fits and the noise model; it does not solve the Einstein or fluid equations and contains no browser Engine code, paper text or LISA data. ## Keep reading Phase-transition gravitational waves · Reading path ### From bubble nucleation to the spectrum LISA could see 1. [You are here **What a bubbling early universe would leave in gravitational waves**](https://sandboxphysics.com/stories/phase-transition-gravitational-waves/what-a-bubbling-early-universe-leaves-in-gravitational-waves/) 2. [Article **How bubbles appear and fill space**](https://sandboxphysics.com/stories/phase-transition-gravitational-waves/how-bubbles-appear-and-fill-space/) 3. [Article **How bubble walls push the plasma**](https://sandboxphysics.com/stories/phase-transition-gravitational-waves/how-bubble-walls-push-the-plasma/) 4. [Article **From the sound lifetime to the spectrum today**](https://sandboxphysics.com/stories/phase-transition-gravitational-waves/from-sound-lifetime-to-the-spectrum-today/) 5. [Article **Recompute a benchmark sound-wave spectrum**](https://sandboxphysics.com/stories/phase-transition-gravitational-waves/recompute-a-benchmark-sound-wave-spectrum/) 6. [Article **Read the LISA sound-wave template and its limits**](https://sandboxphysics.com/stories/phase-transition-gravitational-waves/read-the-lisa-sound-wave-template-and-its-limits/)