Could they explain gravitational wave signals?

A new study published in Physical Review Letters explores the possibility that a strongly supercooled first-order phase transition in the early universe could explain the 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 black hole mergers.

They were first detected by LIGO in 2016, confirming Einstein’s predictions nearly a century later. The most common sources of black holes are merging black holes, rotating neutron stars, and supernovae.

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

SGWBs are different because they are isotropic, meaning they spread evenly in all directions, suggesting that their sources are evenly distributed throughout the universe.

This finding prompted scientists in PRL study to investigate the origin of these waves, which could come from first-order phase transitions (FOPTs) in the early universe.

Phys.org spoke with the study’s 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 probe into the early universe is limited to the period after the formation of the CMB [cosmic microwave background]. Although we have some indirect indications of what happened before the CMB, gravitational waves are currently the only method to probe the very early universe,” Yongcheng said.

Prof. Lei added, “In the past few years, supercooled FOPT has been widely considered as a possible source of SGWB.”

“The new signal observed by PTA may be evidence that this is happening – a very exciting possibility,” said Prof. Athrone.

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

First order phase transitions

FOPTs are phase transitions in which the system transitions between different phases suddenly or intermittently. One such example that we see in our daily life is the freezing of water.

“Water can remain in a liquid state even when the temperature is below freezing. Then with a small deviation [change], suddenly turns to ice. The key feature is that the system remains in the phase for a long time below the transition temperature,” Professor Yongcheng explained.

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 – the breaking of the electroweak symmetry that predicts all weak nuclear interactions – generates the masses of all the fundamental particles we have observed today,” said Prof. Athrone.

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

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

A potential mechanism for generating SGWB

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

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

At this temperature, quantum fluctuations (random motions) 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 FOPT of false vacuum to true vacuum has occurred.

Once nucleated, these bubbles of true vacuum grow and expand. They can collide and merge, or seep through space. Percolation refers to the creation of an interconnected network of true vacuum regions.

The phase transition is complete when a sufficient fraction of the universe is in a state of true vacuum. This completion usually requires the bubbles to seep through a significant portion of the universe.

During this process, the collisions and dynamics of expanding bubbles generate the SGWBs observed by the NANOGrav collaboration.

Modification of the Higgs potential

The work of the researchers began with the creation of a theoretical model for the study of supercooled FOPTs and the possibility of generating SGWBs.

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

The researchers began by modifying the Higgs potential, which explains how the Higgs field interacts with itself and with 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 for studying problems fitting a nano Hz (nHz) signal (detected by the NANOGrav collaboration) to this cubic potential:

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

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

On the other hand, reference points explain the challenges for supercooled FOPT to generate SGWB.

Limitations of the model

The researchers identified two main issues that rule out the supercooled FOPT model as an explanation for the nHz signal detected by the NANOGrav collaboration.

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

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

“Only a few bubbles form, which do not grow fast enough to fill the universe,” explained Prof. Athrone.

Therefore, the completion of a phase transition, where the entire universe moves into a new phase, becomes less likely.

The second problem is reheating. Even considering a scenario where completion is somehow achieved, the energy released during the phase transition releases heat into space. This process increases the temperature of space, a process known as reheating.

“This makes it difficult to maintain the conditions necessary for SGWB production,” added prof. Leia.

Gravitational waves produced in this scenario will not have the same frequency as the waves observed by PTA, typically in the nHz range.

Conclusion and future work

A supercooled FOPT as an explanation for SGWB can help to avoid limitations on standard model modifications and connect the nHz signal to new higher-scale physics, such as those involved in or beyond the electroweak phase transition.

However, as the researchers have shown, the problems suggest that the supercooled 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 and thus further produce nHz gravitational wave signals, it could naturally account for such low-frequency gravitational wave signals,” explained Prof. Chih-Ting.

Prof. Yongcheng added: “The supercooled phase transition can trigger the formation of primordial black holes, which may be part of the dark matter of our universe. The violent process of supercooled FOPT and the much higher energies released during the procedure can also provide an environment for particle production, which is much more important if 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 in this work.

“We plan to release public software with a complete calculation from the particle physics model to the gravitational wave spectra that is fully state-of-the-art and as accurate as it can be achieved today, so other teams can easily apply the same level of rigor as we have,” concluded Prof. Athrone.

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