Decoherence may lock quantum fields into false vacua across the cosmos

The vacuum of the Universe is not the simple emptiness of everyday intuition. In cosmology, a vacuum is a state in which a quantum field rests at a minimum of its energy, and as David Wands, Professor at the Institute of Cosmology & Gravitation at the University of Portsmouth, explains, “When we talk about a vacuum in cosmology, we do not mean completely devoid of energy. A vacuum is rather a state in which a field sits at a minimum of its energy. The true vacuum is the lowest possible minimum, but there can also be local minima, which we call false vacua.” The picture that emerges is a landscape of valleys of different depths, where the deepest depression represents the true vacuum and the shallower ones represent false vacua. Something that settles into one of these shallower depressions can remain trapped there even though a lower-energy configuration exists elsewhere in the landscape. Quantum fields, the fundamental physical objects that permeate the Universe and whose excitations appear to us as particles, can find themselves in precisely this situation, and which valley a field ultimately occupies has profound consequences for the physics of everything that follows.

A new study published in the Journal of Cosmology and Astroparticle Physics by Robson Christie, Jaewoo Joo, Greg Kaplanek, Vincent Vennin and David Wands used a simplified cosmological model to investigate what determines which vacuum a field may end up in within an expanding Universe. The stakes of this question are illustrated by the most famous example the authors themselves invoke: the Higgs field. The vacuum value of the Higgs field contributes to giving mass to the particles of the Standard Model, the theory that describes the known elementary particles and three of the four fundamental forces, and it helps determine the structure of low-energy physics. According to some calculations based on the Standard Model, it is possible that the Higgs field does not sit in the lowest possible energy state but in a false vacuum, while at very large field values a second, deeper minimum may exist. The study is not directly about the Higgs field, but it uses the Higgs as a concrete example of what can happen when a field becomes trapped in a local minimum even though a lower-energy state is available.

“In principle, a transition to that deeper minimum would take the Universe into a radically different state, in which the structure of matter and the forces that govern it would be altered,” explains Robson Christie, a researcher at the School of Mathematics and Physics at the University of Portsmouth and first author of the study. Classically, such a transition would require the field to climb over the energy barrier separating the two minima, like a ball rolling out of a shallow valley and over a mountain before it can descend into a deeper one. Quantum mechanics changes this picture fundamentally. The state of a quantum system can extend beyond the barrier, leaving a small but nonzero probability that the system will simply appear on the other side. This phenomenon, quantum tunnelling, is the mechanism by which a field in a false vacuum could, in principle, escape to the true vacuum, and it has long been a central concern in calculations of vacuum stability in the early and late Universe.

What distinguishes the new work is its treatment of isolation. Many standard calculations of tunnelling treat the field as completely cut off from its surroundings, an idealisation that the authors argue is physically misleading. “We know, however, that perfect isolation is an idealisation,” says Greg Kaplanek, a researcher at Syracuse University in New York. In reality, fields continuously interact with other fields and with whatever surrounds them, in other words with their environment. Kaplanek draws an analogy from laboratory physics: “Think, for example, of quantum computers: we go to enormous lengths to protect the quantum information stored in these machines from the environment, because even weak interactions with it can quickly alter the quantum state. Something similar happens in cosmology: a field is never really alone.” These interactions produce decoherence, the process by which a quantum system that can exist in a superposition of different possibilities gradually loses the ability to maintain that superposition and begins to behave more and more like an ordinary classical system. Using the analogy of a coin, a quantum state is not simply heads or tails but includes both possibilities at once, and interaction with the environment makes it increasingly difficult to preserve such a combination.

In the model constructed by Christie and colleagues, the environment is represented by other fields interacting with the main field under study. The main field can initially be in a quantum superposition involving both vacua, so the framework allows the researchers to track how the competition between the two minima evolves when the field is coupled to its surroundings. One of the surprises of the study is that the environment does not appear to play a decisive role in the initial choice of vacuum. Instead, what matters far more is whether the field is light or heavy relative to the Hubble scale, the characteristic rate at which the Universe is expanding. This comparison between the intrinsic dynamics of the field and the speed of cosmic expansion turns out to govern which minimum the field is likely to settle in during the expansion of space.

“A field that is heavy compared with the Hubble scale can quickly adjust to the changes as the Universe expands,” Christie explains, “and in this case it is highly likely to move towards the true vacuum, the deepest energy minimum.” Heavy fields, in this sense, have enough time during each doubling of cosmic scale to relax toward their lowest-energy configuration, so the expansion does not outpace their internal dynamics. Something quite different happens for lighter fields. “If the expansion is too rapid compared with the dynamics of the field, the system cannot keep up with the changes,” Christie continues. “In this case there can remain a significant probability that the field will also end up in the false vacuum.” In other words, the initial choice between the true and false vacuum is influenced mainly by the relationship between the field’s own dynamics and the rate of cosmic expansion, rather than by the details of the environmental coupling. A rapidly expanding Universe can effectively freeze a light field before it has had the opportunity to find the deepest valley in its energy landscape.

The second half of the story concerns what happens after a light field has landed in a false vacuum. In a perfectly isolated quantum system, tunnelling towards the deeper minimum would still be possible, however slowly. But in the authors’ model, interaction with the environment produces decoherence and destroys the quantum properties needed to maintain a coherent superposition between the two vacua. “The interesting thing is that it is not primarily the environment that decides where the field will end up,” Kaplanek explains. “Once the field has localised in one of the two minima, however, decoherence tends to keep it there. Tunnelling towards the other vacuum is strongly suppressed.” The authors call this phenomenon cosmic lockdown: a kind of lock that stabilises the field in whichever vacuum it has reached, preventing the slow quantum leakage that would otherwise, over vast timescales, allow transitions between minima.

The physical interpretation of cosmic lockdown connects it to a well-established quantum effect. The authors understand it as a manifestation of the quantum Zeno effect, the counterintuitive result that a quantum system which is continuously monitored can have much more difficulty moving from one state to another, because each measurement effectively resets its evolution. Of course, no one is literally observing the cosmological field in the model, and no conscious observer is required. “You do not need a conscious observer,” Kaplanek explains. “The environment continuously gathers information about the state of the system. This process destroys the coherence between the two possible vacua and makes tunnelling from one to the other much more difficult.” In this sense, the rest of the Universe acts as an ever-present measuring apparatus, constantly extracting information about the field’s state and, as a byproduct of that information gathering, freezing it in place. The effect is a striking example of how openness to the environment, usually seen as a nuisance in quantum technology, can instead act as a stabilising force on cosmological scales.

The work remains a simplified model, and the authors are careful not to overclaim its reach. The study does not show that our current Higgs vacuum is protected by cosmic lockdown, and translating the result into a statement about the actual stability of the Higgs field would require more realistic treatments of the many interactions present in the early and late Universe. The result does, however, establish an interesting principle: interactions with the environment can make a false vacuum more stable by suppressing tunnelling towards another state, reversing the usual intuition that openness always undermines stability. “If a mechanism of this kind were relevant in more realistic cosmological situations, then it could help stabilise a field that is already sitting in a false vacuum,” Wands concludes. “But understanding how far this can be applied to the Higgs field will require more realistic models.” If our Higgs field really is sitting in a false vacuum, as some Standard Model calculations suggest may be the case, then cosmic lockdown points to at least one reassuring possibility: the ceaseless interaction of the field with its surroundings could help make a transition to a radically different state, one in which the structure of matter and the forces governing it would be altered, even more difficult than existing tunnelling estimates imply.

Subject of Research: Decoherence-induced suppression of quantum tunnelling between false and true vacua in an expanding Universe

Article Title: Cosmic lockdown: how the environment can isolate quantum fields

Article References: Cosmic lockdown: how the environment can isolate quantum fields. (n.d.). Original publication

Image Credits: AI Generated

DOI: Not provided

Keywords: cosmology, quantum fields, decoherence, false vacuum, quantum tunnelling, Higgs field, quantum Zeno effect, vacuum stability, Hubble scale, Standard Model, early Universe, JCAP