When we look up at the night sky, we see stars, galaxies, and glowing nebulae—but most of the universe is invisible. Astronomers know that almost 85% of all matter is dark matter, a mysterious form that doesn’t give off light but shows its presence through gravity.
Over the years, scientists have proposed many ideas about what dark matter could be—new particles, exotic forms of matter, or even something more familiar but hidden. One fascinating possibility is that dark matter is made up of black holes—not the ones formed by dead stars, but ancient ones that were born in the very early universe. These are called Primordial Black Holes (PBHs).
PBHs were first imagined in the late 1960s and early 1970s by scientists like Zel’dovich, Novikov, and Hawking. They proposed that during the first fractions of a second after the Big Bang, some regions of space could have been dense enough to collapse under their own gravity, forming black holes.
These early black holes could vary hugely in size—from tiny ones smaller than a mountain to enormous ones millions of times heavier than the Sun. Over time, they might have played many roles in shaping the universe:
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They could be the dark matter that holds galaxies together.
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They might explain the black hole mergers detected by gravitational wave observatories like LIGO and Virgo.
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The largest ones could even be the seeds of supermassive black holes found in the centers of galaxies.
But despite these exciting possibilities, one big question remains: how exactly did these primordial black holes form?
The Challenge: Explaining How PBHs Formed
For a long time, most theories said that PBHs were created from density fluctuations in the early universe. These fluctuations were tiny variations in how matter and energy were spread out during inflation—a period of extremely rapid expansion that happened right after the Big Bang.
In simple terms, if one small patch of space was slightly denser than its surroundings, gravity could make that region collapse into a black hole after inflation ended.
This explanation is reasonable, but it comes with some problems:
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It requires a very precise tuning of conditions. The density fluctuations need to be just right—too small, and nothing collapses; too large, and the universe wouldn’t look the way it does today.
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It predicts too wide a range of black hole masses. Many of these models create PBHs with lots of different sizes, but observations suggest that if PBHs exist, they probably have masses in a narrow range.
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It would produce extra gravitational waves. These waves should be detectable with pulsar timing experiments, but current data haven’t shown clear signs of them.
Because of these issues, scientists have been exploring other ideas—ones that don’t rely only on density ripples.
A New Idea: Black Holes Born from Collapsing Bubbles
Another possible way to make PBHs involves vacuum bubbles.
In the early universe, the “vacuum” isn’t empty. It has energy, and the energy can exist in different states. One of these states can be a false vacuum—a temporary, unstable state of energy. Eventually, the universe can “tunnel” from this false vacuum to a true vacuum, a lower-energy, more stable state.
This process is a bit like water freezing: the false vacuum is the liquid state, and the true vacuum is the solid ice. When freezing starts, tiny bubbles of the new phase appear and grow. In the universe, when bubbles of true vacuum appear during this transition, they can expand or collapse depending on the surrounding conditions.
If these bubbles collapse under their own gravity after inflation, they can form primordial black holes.
This bubble-collapse idea is not new—it was studied by scientists like Garriga, Vilenkin, and Kusenko. However, earlier models had a problem: they assumed that the rate of bubble formation stayed the same over time. This led to a broad range of black hole masses, which doesn’t match what we expect for dark matter or LIGO’s black hole data.
That’s where a new study by Wang, Zhang, and Suyama comes in.
The New Model: Two Fields Working Together
Wang, Zhang, and Suyama proposed a two-field model of the early universe. In this model, two special fields—the inflaton and the instanton—interact in a very specific way.
1. The Inflaton Field (χ): Driving Inflation
The inflaton field, usually written as χ (chi), is the field that caused inflation. During inflation, this field slowly rolled down its potential energy curve, making the universe expand extremely fast and become smooth and flat.
2. The Instanton Field (ϕ): Triggering Bubble Formation
The second field, written as ϕ (phi), acts like an “instanton” field. It controls when and how bubbles of true vacuum appear inside the false vacuum. These bubbles are quantum fluctuations—tiny pockets where the universe briefly “decides” to change its energy state.
3. The Key: A Special Coupling Between the Two Fields
The key idea in the Wang–Zhang–Suyama model is that the instanton field ϕ is non-minimally coupled to the inflaton field χ. This means that the behavior of ϕ depends on the value of χ. The strength of this coupling is described by a function called g(χ).
As inflation continues, χ changes over time, and so does g(χ). At a certain point—when χ reaches a special value called χ*—the difference in energy between the false vacuum and the true vacuum becomes the largest.
This difference controls how easily bubbles of true vacuum can appear. When the difference is largest, the tunneling rate (the probability of bubble formation) reaches its maximum.
That means most bubbles form around this time, near χ = χ*.
What Happens After Inflation Ends
After inflation ends, the universe’s conditions change dramatically. The energy of the false vacuum drops below that of the true vacuum. In other words, what was once the “lower” energy state becomes the “higher” one.
Because of this change, the bubbles that formed earlier now find themselves unstable—they can no longer expand. Instead, they collapse under their own gravity.
These collapsing bubbles can turn into primordial black holes.
Since most bubbles formed around the same time (when χ = χ*), the resulting black holes have almost the same mass. This gives a sharp peak in the PBH mass distribution—a nearly monochromatic spectrum.
This feature is important because it matches what many scientists believe about PBHs: if they exist, they probably come in a narrow range of masses, rather than being spread over many different sizes.
The Physics Behind Bubble Formation
The creation of these bubbles is described by two well-known quantum processes:
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Coleman–De Luccia (CDL) Tunneling:
This process describes how a field can tunnel from the false vacuum to the true vacuum when gravity is taken into account. The field effectively “borrows” energy from quantum fluctuations to pass through an energy barrier. -
Hawking–Moss (HM) Transition:
In this case, the field climbs over the barrier rather than tunneling through it, like rolling over a hill due to thermal fluctuations.
In their paper, Wang, Zhang, and Suyama studied both these processes in their model. They found that CDL tunneling usually dominates, meaning that the vacuum transitions mainly happen through quantum tunneling rather than thermal jumps.
They also calculated the tunneling rate, which depends on the “action” of the instanton—a mathematical quantity that measures how difficult it is for the field to move from one state to another. The smaller this action, the easier the tunneling.
Interestingly, the authors discovered that the tunneling action is smallest exactly when χ = χ*. That means tunneling—and therefore bubble creation—is most likely at that moment.
This gives a natural explanation for why the PBH mass distribution is so sharply peaked.
Different Types of PBHs in the Model
By adjusting the parameters of the model, especially the form of the coupling function g(χ) and the value of χ*, the authors can predict different outcomes:
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Small PBHs: With masses below that of the Sun. These could serve as dark matter, filling galaxies without emitting light.
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Stellar-Mass PBHs: Around a few to tens of solar masses. These could explain the black hole mergers detected by gravitational wave observatories like LIGO and Virgo.
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Supermassive PBHs: With millions or billions of solar masses. These could act as the seeds of the giant black holes at the centers of galaxies.
This flexibility makes the model very powerful. A single physical mechanism could explain several major cosmic phenomena just by changing how the two fields interact.
Why This Model Is Special
1. No Need for Enhanced Curvature Perturbations
Most other PBH models require very large fluctuations in the curvature (or density) of space during inflation. These fluctuations would also produce strong gravitational waves that should be detectable.
However, the two-field model by Wang, Zhang, and Suyama doesn’t need those large fluctuations. The PBHs come from bubble collapse, not from density peaks.
That means even if future gravitational wave observatories don’t detect the expected background from enhanced perturbations, PBHs could still exist—formed quietly through this two-field mechanism.
2. A Narrow, Predictable Mass Range
Earlier models often produced PBHs with a wide range of masses, which doesn’t match most observations. The new model naturally gives a sharp, narrow mass peak, which is exactly what astrophysicists are looking for.
3. Works Within Known Physics
The model doesn’t require any new particles beyond what’s already allowed in standard inflationary theory. It simply uses two interacting fields—a concept already common in modern cosmology.
Caveats and Future Work
To make their analysis manageable, the authors simplified their calculations. They treated the system as two separate single-field models: one for inflation (χ) and one for tunneling (ϕ).
In reality, the two fields interact at the same time. A complete picture would require solving their combined dynamics numerically. Previous studies suggest that in multi-field systems, tunneling can happen slightly more easily because the field can find a “shortcut” through the energy landscape.
If this effect is included, it might slightly change the predicted PBH mass or broaden the mass peak a little. The authors plan to study this more detailed version in future work.
Big Picture: Why This Matters
This model does more than just explain how black holes might have formed—it connects several big ideas in cosmology into one elegant framework:
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It links inflation and black hole formation. The same period that shaped the universe’s large-scale structure may also have created its smallest and densest objects.
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It offers a possible dark matter candidate. If the resulting PBHs have the right masses, they could make up all of the universe’s dark matter.
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It explains different cosmic black holes at once. By changing only a few parameters, the model can produce both stellar-mass and supermassive black holes.
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It provides testable predictions. Even though it doesn’t predict large gravitational wave signals, future observations—such as microlensing or PBH evaporation—could help confirm or rule out this scenario.
Conclusion: A Subtle Harmony of the Early Universe
The early universe was a place of unimaginable energy and rapid change. Fields interacted, expanded, and fluctuated, setting the stage for everything we see today.
The model proposed by Wang, Zhang, and Suyama shows that something as simple as the interaction between two fields—the inflaton and the instanton—could have quietly created black holes long before stars and galaxies existed.
As these bubbles of true vacuum formed and collapsed, they may have left behind the first black holes, some of which could still be around today—shaping galaxies, merging in distant space, or hiding as dark matter.
This two-field model doesn’t just offer a new theory; it offers a new way of thinking about the birth of structure in the universe. It reminds us that even in the earliest fractions of a second after the Big Bang, the universe’s future was already being written—in the delicate dance of two invisible fields.
Reference: Haonan Wang, Ying-li Zhang, Teruaki Suyama, "Nearly Monochromatic Primordial Black Holes as total Dark Matter from Bubble Collapse", Arxiv, 2025. https://arxiv.org/abs/2510.19233
🧠 Key Technical Terms
1. Primordial Black Holes (PBHs)
These are black holes that may have formed in the very early universe, just after the Big Bang.
Unlike normal black holes that come from collapsing stars, PBHs could form when very dense regions of space collapsed under their own gravity billions of years ago.
They can have a wide range of sizes — from very tiny ones lighter than a mountain to gigantic ones heavier than millions of Suns.
2. Dark Matter
Dark matter is a mysterious type of matter that doesn’t give off light or energy, so we can’t see it directly.
We know it’s there because its gravity affects how galaxies move and how light bends around them.
Scientists believe that PBHs might make up some or all of this invisible dark matter.
3. Inflation
Inflation was a short period right after the Big Bang when the universe expanded extremely fast — much faster than the speed of light (though this doesn’t break physics laws because it’s space itself that expanded).
This rapid expansion made the universe smooth and uniform while also spreading out tiny quantum fluctuations that later grew into galaxies and stars.
4. Fields (in Physics)
In physics, a field is something that fills space and can have a value at every point.
For example, the temperature field of a room tells you what the temperature is at every spot in the room.
In cosmology, fields describe quantities like energy or forces that filled the early universe.
5. Inflaton Field (χ or Chi)
This is the special field responsible for inflation.
You can think of it like a ball rolling down a hill: as the ball rolls (the field changes), the energy of the universe changes, causing rapid expansion.
The inflaton controls how fast inflation happens and when it ends.
6. Instanton Field (ϕ or Phi)
This second field appears in Wang, Zhang, and Suyama’s model.
It’s responsible for quantum tunneling — a process where the universe can switch from one energy state (false vacuum) to another (true vacuum).
The instanton field tells us when and how “bubbles” of the new energy state form.
7. Vacuum
In everyday language, “vacuum” means empty space.
But in physics, vacuum means the state of lowest possible energy — not truly empty, but full of quantum activity.
There can be different types of vacuums depending on how energy is arranged in the universe.
8. False Vacuum and True Vacuum
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A false vacuum is a temporary, unstable state of energy. The universe can stay in it for a while but will eventually “decay” to a lower-energy state.
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A true vacuum is a stable state — it has the lowest possible energy.
When the universe moves from the false vacuum to the true vacuum, it releases energy, and bubbles of true vacuum form and grow.
Think of it like supercooled water that suddenly starts freezing — bubbles of ice form inside the water.
9. Vacuum Bubbles
These are small regions (or “bubbles”) where the universe has transitioned from false vacuum to true vacuum.
They appear due to quantum effects and can either expand or collapse.
In Wang, Zhang, and Suyama’s model, when these bubbles collapse after inflation, they form primordial black holes.
10. Quantum Tunneling
This is a strange but real effect from quantum physics.
Normally, a particle stuck in a valley between two hills needs enough energy to climb over a hill. But quantum mechanics allows the particle to “tunnel through” the hill even without enough energy — like a ghost passing through a wall.
In the early universe, this kind of tunneling allowed the universe to jump from the false vacuum to the true vacuum.
11. Coupling (and Non-Minimal Coupling)
Coupling means two fields or particles interact or influence each other.
If one field changes, it affects the other.
Non-minimal coupling means the relationship is not simple — it depends on a function (in this case, g(χ)) that changes over time.
In this model, the instanton field ϕ is non-minimally coupled to the inflaton χ. This means that as the inflaton changes during inflation, it also changes how easily bubbles can form.
12. The Coupling Function (g(χ))
This is a mathematical function that describes how strongly the two fields interact.
It changes as the inflaton field χ changes.
At a certain value of χ (called χ*), this function reaches its maximum, meaning bubble formation happens most easily.
13. χ* (Chi-Star)
This special value of the inflaton field is the moment when bubble creation is strongest.
At χ = χ*, the difference in energy between the false and true vacuums is the largest, so most bubbles are created at that time.
14. Tunneling Rate
This tells us how likely it is for bubbles of true vacuum to appear at a given moment.
A higher tunneling rate means bubbles form more easily and more often.
In this model, the tunneling rate reaches its maximum when χ = χ*.
15. Coleman–De Luccia (CDL) Instanton
This is a solution in physics that describes how a vacuum bubble forms when gravity is included.
It’s a type of quantum tunneling process where the universe tunnels from the false vacuum to the true vacuum.
In this model, most of the bubble formation happens through CDL instantons.
16. Hawking–Moss (HM) Instanton
This is another type of vacuum transition.
Instead of tunneling through the barrier, the field jumps over it — like a ball gaining enough energy to roll over a hill instead of going through it.
This process is usually slower than the CDL process.
17. Potential (Energy Landscape)
A potential describes how energy changes with the value of a field.
It’s often shown as a curve with hills and valleys:
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Valleys represent stable states (like true vacuum).
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Hills represent barriers (energy obstacles).
The shape of the potential determines how inflation and tunneling happen.
18. Mass Function of PBHs
This shows how many PBHs form with different masses.
If it’s broad, PBHs come in many different sizes.
If it’s narrow or sharply peaked, most PBHs have nearly the same mass.
In this model, the mass function is sharply peaked, meaning all PBHs formed around the same size.
19. Gravitational Waves (GWs)
Gravitational waves are ripples in space-time caused by massive objects accelerating (like black holes merging).
Some PBH models predict extra gravitational waves from large early-universe fluctuations, but Wang, Zhang, and Suyama’s model does not — which fits well if we don’t detect those waves in future experiments.
20. Induced Gravitational Waves (IGWs)
These are gravitational waves that are second-hand effects — they’re generated by big density fluctuations in the early universe.
Since this model doesn’t rely on those fluctuations, it doesn’t produce strong IGWs.
21. Cold Dark Matter (CDM)
This is the form of dark matter that moves slowly (hence “cold”) and interacts only through gravity.
PBHs are a natural candidate for CDM because they don’t emit light or radiation.
22. Inflationary Potential Difference
This term refers to how much energy difference there is between the false vacuum and the true vacuum during inflation.
A bigger difference means stronger tunneling and more bubble creation.
23. Multi-field Dynamics
This refers to how two or more fields (like χ and ϕ) change together over time.
It’s more complex than single-field models because the fields can affect each other’s movement through their energy landscape.
24. Action (in Quantum Physics)
“Action” is a quantity that helps determine how likely a process is to occur in quantum mechanics.
In tunneling, a smaller action means the process happens more easily.
In this model, the action is smallest at χ = χ*, which is why most bubbles form there.
25. Monochromatic Spectrum
“Monochromatic” literally means “one color,” but in this context, it means one mass or one size.
A monochromatic PBH spectrum means that almost all PBHs formed with the same mass, instead of a wide variety of masses.
26. Gravitational Collapse
When an object (like a bubble or a dense region of space) becomes too heavy for its internal pressure to support it, gravity pulls it inward until it collapses.
If it collapses completely, it becomes a black hole.
27. Parameter Tuning
In physics models, parameters are adjustable numbers that describe how strong a coupling is, how fast inflation happens, etc.
“Tuning parameters” means adjusting these values to see what kinds of results (like PBH masses) the model produces.
28. Stochastic Gravitational Wave Background
This is a faint “hum” of gravitational waves coming from all directions, made up of many overlapping sources.
Some PBH models predict that this background should be detectable.
However, the two-field model predicts no strong background, so the absence of such a signal wouldn’t rule it out.
29. Potential Barrier
In the energy landscape, this is the “hill” separating the false vacuum from the true vacuum.
The field needs to tunnel through or jump over this barrier to move to the lower-energy state.
30. Energy Difference Between FV and TV
This is how much lower (or higher) the true vacuum’s energy is compared to the false vacuum’s energy.
It determines how easily tunneling happens — a bigger difference makes it easier for the field to switch states.
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