Gravitational Waves From Early Universe Phase Transitions

Principal Investigator:
David Weir

Department of Mathematics and Natural Sciences, University of Stavanger (Norway)

Local Project ID:

HPC Platform used:
Hazel Hen of HLRS

Date published:

Gravitational waves are ripples in spacetime, predicted by Einstein already a century ago. With the announcement earlier this year that gravitational waves had been successfully detected from two black holes merging, attention now turns to other potential sources of gravitational waves. Such sources include dramatic events that may have occurred very early in the history of the universe. Understanding these other sources also informs the design of future gravitational wave detectors, such as the European Space Agency (ESA) project eLISA.

As the universe expanded and cooled, about a nanosecond after the big bang, the Higgs field found a new minimum energy configuration into which it could settle -- one which gave it mass and, in turn, made other particles massive too. In the Standard Model of particle physics, this change is very gentle and termed a crossover.

However, we know that the Standard Model is incomplete -- specifically, it does not adequately explain why there is more matter than antimatter in the visible universe. To explain the asymmetry, it is necessary amongst other things that the universe was out of equilibrium for a time. One way to achieve this would be for the universe to have undergone a more dramatic phase transition when the Higgs became massive; this is a feature of many models which extend the Standard Model. In such a scenario, bubbles of the massive Higgs phase would nucleate and expand in a hot plasma of lighter particles until the bubbles merged, filling the whole universe.

The expanding walls of these bubbles would set up shock waves in the plasma, and even after the bubbles had collided these shock waves would live on as sound waves in the plasma until it expanded and cooled down.

Both the collision of the bubbles, and the interaction of the sound waves afterwards, would be very violent processes. They would involve rapidly time-varying distributions of mass and energy, precisely the conditions that Einstein's equations predict will produce gravitational waves. If the phase transition was violent enough, it would be detectable by future gravitational wave detectors such as eLISA.

Simulating such a phase transition is not easy. The sound waves are propagating in a plasma with fluid velocities that can be a substantial fraction of the speed of light. In addition, there are many length scales that need to be separated; in the real universe, there would be many orders of magnitude between the width of the walls and the size of the universe, but even on the largest supercomputers today these can only be separated by a factor of a hundred. Running the code on Hazel Hen, in some of the largest simulations of the dynamics of the early universe ever attempted, yielded the best understanding yet of the underlying processes.

These cosmological events would have happened on scales much too large for detection by earth-based gravitational wave projects such as LIGO or VIRGO, or indeed the Einstein Telescope, but they are perfectly placed to be observed from space, where the arms of the detector can be millions of kilometres long rather than just a few kilometres, as on Earth.

These are exciting times: gravitational waves are a brand new tool for exploring astrophysics and cosmology. As eLISA moves towards final approval and then launch, it is important that we understand what cosmological processes could be detected and which design of mission represents the best prospects for scientific discovery. The results of this project fed into a report by the Cosmology Working Group, which in turn influences the mission profile.

Further Reading:

There is a popular article about this work available at:


This research project was made possible through computing time granted by PRACE (Partnership of Advanced Computing in Europe). HPC system Hazel Hen of the High Performance Computing Center Stuttgart (HLRS) served as computing platform for this simulation project.

Scientific Team:

David Weir (PI), Department of Mathematics and Natural Sciences, University of Stavanger, Norway, Mark Hindmarsh, University of Sussex and University of Helsinki; Kari Rummukainen, University of Helsinki.


1. Revisiting the envelope approximation: gravitational waves from bubble collisions 
David J. Weir, Phys.Rev. D93 (2016) no.12, 124037, DOI: 10.1103/PhysRevD.93.124037 arXiv:1604.08429

2. Science with the space-based interferometer eLISA. II: gravitational waves from cosmological phase transitions 
Chiara Caprini et al., JCAP 1604 (2016) no.04, 001, DOI: 10.1088/1475-7516/2016/04/001 arXiv:1512.06239.

3. Numerical simulations of acoustically generated gravitational waves at a first order phase transition 
Mark Hindmarsh, Stephan J. Huber, Kari Rummukainen, David J. Weir, Phys.Rev. D92 (2015) no.12, 123009, DOI: 10.1103/PhysRevD.92.123009 arXiv:1504.03291.

4. Gravitational waves from the sound of a first order phase transition
Mark Hindmarsh, Stephan J. Huber, Kari Rummukainen, David J. Weir, Phys.Rev.Lett. 112 (2014) 041301, DOI: 10.1103/PhysRevLett.112.041301 arXiv:1304.2433.

Further results will be reported in papers later this year.

Scientific Contact:

Dr. David J. Weir
Department of Mathematics and Natural Sciences, University of Stavanger
4036 Stavanger (Norway)
email: [@]

Tags: HLRS Astrophysics University of Stavanger