Can they explain gravitational wave signals?

A new study published in Physical review papers explores the possibility that a supercooled first-order phase transition in the early universe could explain the gravitational wave signals observed by pulsar time 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 merging black holes.

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

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

SGWBs are different because they are isotropic, meaning they propagate equally in all directions, indicating that their source is uniformly distributed throughout the universe.

This discovery prompted scientists to PRL study to explore the origin of these waves, which may be from the first-order phase transition (FOPT) in the early universe.

Phys.org spoke with the co-authors of the study, 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 hints about what happened before the CMB, gravitational waves are currently the only method to probe the very early universe,” Yongcheng said.

Prof. Lei added, “In recent years, supercooled FOPT has been widely considered a potential source of SGWB.”

“A new signal seen by PTAs may be evidence of this 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 weak symmetry breaking mechanism. “Relating gravitational wave signals of different frequencies to cosmic phase transitions has opened another window for me to study this,” he said.

First order phase transitions

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

“Water can remain liquid even if the temperature is below freezing. Then, with a little worry [change], suddenly turns into ice. The main signature is that the system remains in the phase for a long time below the transition temperature”, explained Prof. Yongcheng.

The electromagnetic 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, a 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. Athron.

This led to the separation of the weak electromagnetic force into the electromagnetic and weak forces via the Higgs field (which gives all particles their mass). The process by which this occurs is the first-order strong electroweak 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 by the NANOGrav collaboration.

Possible mechanism for generation of SGWB

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

As the universe expands and cools, the potential energy decreases. Below a 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 regions where FOPT of false vacuum to true vacuum has occurred.

Once nucleated, these true vacuum bubbles grow and expand. They can collide and merge, eventually penetrating space. Percolation refers to the formation of a connected network of true vacuum regions.

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

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

Modification of the Higgs potential

The researchers’ work began by building a theoretical model to study 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 began by modifying 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 (discovered by the NANOGrav collaboration) to this cubic potential:

1. The penetration temperature is the temperature at which bubbles of the true vacuum state nucleate and grow large enough to form a connected network throughout the universe.
2. The termination temperature is the temperature at which the phase transition is completely complete, with the entire universe transitioning to the true vacuum state.
3. Benchmark 1 represents a scenario with a significant degree of supercooling, while meeting the penetration and termination criteria.
4. Reference point 2 represents a scenario where the strongest supercooling is achieved with a nominal percolation temperature of about 100 MeV, but does not meet the real percolation criteria and does not complete the transition.

The two measures of temperature are essential to understand the dynamics and timing of the phase transition. They ensure that the transition is comprehensive and complete, which is necessary for the generation of a gravitational wave signal.

The benchmarks, on the other hand, highlight the challenges for a supercooled FOPT to generate SGWB.

Limitations of the model

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

The first challenge is to penetrate and complete 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 for bubbles of the new phase (true vacuum) to nucleate and grow is low.

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

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

The second challenge is that of rewarming. Even if one considers a scenario where termination 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 reheating.

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

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

Conclusion and future work

Supercooled FOPT as explanations for SGWB can help to avoid limitations in modifications to the Standard Model and connect the nHz signal to new higher-order physics, such as those involved in weak phase transitions or beyond .

However, as the researchers have shown, challenges suggest that the supercooled FOPT may not be the source of the observed SGWB.

The researchers have plans to explore other FOPTs that could explain the observed signal.

“If the unknown dark sector is capable of generating chiral phase transitions similar to those in quantum chromodynamics, further producing nHz gravitational wave signals, it can naturally account for such low-frequency gravitational wave signals,” Prof. explained. Chih-Ting.

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

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 are planning 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 can be achieved today, so that other teams can easily apply the same level of rigor as we have”, concluded Prof. Athron.

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