Supercooled phase transitions: can they explain gravitational wave signals?

A new study published in Physical Assessment Letters explores the possibility that a strongly undercooled first-order phase transition in the early universe could explain gravitational wave signals observed by pulsar timing arrays (PTAs).

Gravitational waves, first proposed by Albert Einstein in his general theory of relativity, are ripples in the fabric of spacetime, caused by violent processes such as the merger of black holes.

They were first discovered by LIGO in 2016 and confirmed Einstein’s predictions almost a century later. The most common sources of black holes are black hole mergers, spinning neutron stars, and supernovae.

Recently, the NANOGrav, or North American Nanohertz Observatory for Gravitational Waves, detected the presence of stochastic gravitational wave background (SGWB) from pulsar timing arrays (PTAs).

SGWB are different because they are isotropic, meaning they spread evenly in all directions, indicating that their source is uniformly distributed throughout the universe.

This finding brought the scientists into the PRL investigating the origin of these waves, which could come from first-order phase transitions (FOPT) in the early universe.

Phys.org spoke to study co-authors Prof. Yongcheng Wu, Prof. Chih-Ting Lu, Prof. Peter Athron and Prof. Lei W from Nanjing Normal University, to learn more about their work.

‘Our research into the early universe is limited to the period after the formation of CMB [cosmic microwave background]. Although we have some indirect clues about what happened before CMB, gravitational waves are currently the only method to explore the very early universe,” said Yongcheng.

Prof. Lei added: “In recent years, the hypothermic FOPT has been widely considered as a possible source of the SGWB.”

“A new signal seen by PTAs could be evidence that this is happening – a very exciting possibility,” said Prof. Athron.

Prof. Chih-Ting said he wanted to understand the connection between the Higgs field and the Higgs boson, and its connection to the mechanism of electroweak symmetry breaking. “Coupling gravitational wave signals of different frequencies with cosmic phase transitions has opened a new window for me to study this,” he said.

First-order phase transitions

FOPT are phase transitions where a system transitions abruptly or discontinuously between different phases. An example of this that we encounter in our daily lives is the freezing of water.

‘The water can remain in a liquid state even when the temperature is below freezing. Then it is possible, with a small disruption [change], it suddenly turns to ice. The main signature is that the system remains in the phase below the transition temperature for a long time,” explains Prof. Yongcheng.

The electroweak force is a unified description of two of the four fundamental forces of nature: the electromagnetic force and the weak nuclear force.

“We know that in our universe, one drastic change – breaking the electroweak symmetry that predicts all weak nuclear interactions – generates the mass of all the fundamental particles we observed today,” said Prof. Athron.

This led to the electroweak force splitting into the electromagnetic and weak forces via the Higgs field (which gives all particles their mass). The process by which this happens is the strong electroweak phase transition of the first order.

A supercooled FOPT is one in which the temperature drop during the phase transition is sudden. The researchers wanted to understand whether such FOPT could be the source of the SGWB observed by the NANOGrav collaboration.

Potential mechanism for generating SGWB

The idea behind the theory is that the early universe was in a high-temperature state known as a false vacuum state, meaning its energy is not the lowest possible energy.

As the universe expands and cools, its potential energy decreases. Below a critical temperature, the false vacuum state becomes unstable.

At this temperature, quantum fluctuations (random movements) can initiate the formation of true vacuum states, which are the lowest energy states. This happens through the process of nucleation (formation) of bubbles.

Bubbles represent areas where the FOPT from false vacuum to true vacuum has occurred.

Once formed, these bubbles of true vacuum grow and expand. They can collide and merge, eventually seeping through space. Percolation refers to the formation of a connected network of true vacuum areas.

The phase transition is complete when a sufficiently large part of the universe is in the true vacuum state. This completion typically requires bubbles to percolate through a significant portion of the universe.

During this process, the collisions and dynamics of expanding bubbles generate SGWB, which the NANOGrav collaboration has observed.

Changing the Higgs potential

The researchers’ work began with building a theoretical model to study the supercooled FOPTs and the possibility of SGWB generation.

Prof. Lei explained: “In the case of supercooled FOPTs, models can predict the conditions under which such transitions can occur, including the temperature at which the phase transition occurs and the characteristics of the transition process.”

The researchers started by tweaking the Higgs potential, which explains how the Higgs field interacts with itself and other fundamental particles.

They added a cubic term to facilitate the dynamics of the supercooled FOPT in the early universe.

Here they define four key parameters to study the challenges of fitting the nano Hz (nHz) signal (detected by the NANOGrav collaboration) with this cubic potential:

1. The percolation temperature is the temperature at which bubbles from the true vacuum state nucleate and grow enough to form a connected network throughout the universe.
2. The completion temperature is the temperature at which the phase transition is completely completed, with the entire universe transitioning to the true vacuum state.
3. Benchmark point 1 represents a scenario with a significant degree of subcooling while meeting the percolation and completion criteria.
4. Benchmark point 2 represents a scenario where stronger subcooling is achieved with a nominal percolation temperature of around 100 MeV, but does not meet realistic percolation criteria and does not complete the transition.

The two temperature measurements are essential for understanding the dynamics and timing of the phase transition. They ensure that the transition is comprehensive and complete, which is necessary for generating a gravitational wave signal.

In contrast, the benchmark points reveal the challenges for a subcooled FOPT to generate SGWB.

Limitations of the model

The researchers identified two key challenges that rule out the undercooled FOPT model as an explanation for the nHz signal detected by the NANOGrav collaboration.

The first challenge is the percolation and completion of the supercooled FOPT. When the temperature of the universe falls below a critical value, the phase transition will not occur.

This is because the energy required to nucleate and grow bubbles of the new phase (true vacuum) is low.

“Only a few bubbles form and they do not grow fast enough to fill the universe,” explains Prof. Athron.

Therefore, the completion of the phase transition, where the entire universe transitions to the new phase, becomes less likely.

The second challenge is that of warming up. Even considering a scenario in which completion is somehow achieved, the energy released during the phase transition releases heat into the universe. This process increases the temperature of the universe, a process known as warming.

“This makes it difficult to maintain the conditions necessary for the production of SGWB,” added Prof. Lei.

The gravitational waves produced in this scenario will not be at the same frequency as those observed by PTAs, typically in the nHz range.

Conclusion and future work

Supercooled FOPT as an explanation for SGWB can help overcome the limitations on modifications to the Standard Model and connect the nHz signal to new larger-scale physics, such as those involved in the electroweak phase transition or beyond.

However, as the researchers showed, challenges suggest that hypothermic FOPT may not be the source of the observed SGWB.

The researchers plan to investigate other FOPTs that could explain the observed signal.

“If the unknown dark sector is able to generate chiral phase transitions similar to those in quantum chromodynamics, thereby further producing nHz gravitational wave signals, it could naturally explain such low-frequency gravitational wave signals,” explains Prof. Chih-Ting.

Prof. Yongcheng added: ‘The supercooled phase transition could trigger the formation of primordial black holes, which could be part of the dark matter component of our universe. The violent process of supercooled FOPT and much higher energy released during the procedure can also provide an environment for particle production, which is much more important when we consider dark matter production.”

Prof. Lei also mentioned exploring broader cosmological implications, such as supermassive black hole binaries.

The researchers also plan to release the software and calculations they developed for this work.

“We plan to release public software with a complete calculation from the particle physics model to the gravitational wave spectra that is completely state-of-the-art and as accurate as is possible today, so that other teams can easily achieve the same level of accuracy can apply as we have done,” concluded Prof. Athron.

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