Scientists have long searched for a particle called the axion, which could help solve one of the biggest mysteries in particle physics. The axion was originally proposed to explain why the strong nuclear force appears to follow an extremely precise symmetry between matter and antimatter.
But there is a major problem.
The same quantum effects of gravity that are expected to exist throughout the universe may also destroy the symmetry that makes the axion solution work.
Now, researchers Takeshita and Yoshioka have studied a possible solution using an unusual combination of wormholes and a modified theory of gravity called Metric-Affine Gravity.
Their work suggests that extra properties of spacetime could make axionic wormholes much weaker sources of symmetry breaking. If this idea works, it could help protect the axion from dangerous quantum-gravity effects.
Why Is the Axion Important?
The axion was proposed to solve a famous problem called the strong CP problem.
The strong nuclear force is described by a theory called quantum chromodynamics (QCD). According to the theory, the strong force could produce effects that violate CP symmetry.
However, experiments show that this effect is incredibly small.
This creates a puzzle: Why does nature appear to protect CP symmetry so strongly in the strong nuclear force?
The Peccei–Quinn mechanism provides a possible answer.
It introduces a new symmetry called Peccei–Quinn (PQ) symmetry. When this symmetry breaks, a new particle called the axion appears.
The axion then interacts with the strong force in a special way. Because of these interactions, the axion naturally moves toward a state where the unwanted CP violation becomes extremely small.
In simple terms, the axion provides a natural mechanism that can push the strong force toward a CP-conserving state.
But this mechanism only works if the PQ symmetry is protected extremely well.
And that is where the problem begins.
Gravity May Break the Axion's Symmetry
Physicists generally expect that quantum gravity does not allow perfect global symmetries to remain completely untouched.
If gravity breaks the PQ symmetry, it can create additional terms in the axion's potential.
Even if these additional effects are extremely small, they could shift the axion away from its ideal position.
That could destroy the solution to the strong CP problem.
This challenge is known as the axion quality problem.
Scientists therefore need a mechanism that keeps gravity-induced PQ symmetry breaking incredibly small.
One possible source of this breaking comes from axionic wormholes.
Wormholes and the Axion
The wormholes discussed in this research are not the science-fiction tunnels often shown in movies.
They are mathematical solutions that appear in certain theories of gravity. More specifically, they are called Euclidean wormholes or gravitational instantons.
These objects can connect two different regions of spacetime through a narrow throat.
Importantly, axionic wormholes can carry Peccei–Quinn charge.
Because of this, they can provide a way for gravity to break the global PQ symmetry.
The strength of this effect depends strongly on something called the wormhole action, represented by S.
The contribution from a wormhole is roughly proportional to:
e⁻ˢ
This means that a larger value of S makes the effect dramatically smaller.
For the axion to remain a good solution to the strong CP problem, researchers generally require the wormhole action to be very large, with a typical requirement of around S ≳ 190.
The bigger the action, the safer the axion is.
Why Ordinary Gravity Has a Problem
Earlier research found that axionic wormholes can have a sufficiently large action in some simplified situations.
For example, if the radial part of the field responsible for the axion is kept fixed, the wormhole action can roughly behave like:
S ~ Mₚ / fₐ
Here, Mₚ represents the Planck scale and fₐ is the axion decay constant.
This can provide strong suppression when the axion decay constant is small enough.
However, the situation changes when the radial part of the field is allowed to move dynamically.
The action can then become much smaller, behaving roughly like:
S ~ log(Mₚ / fₐ)
A logarithm grows much more slowly than a direct ratio.
As a result, the wormhole effect may no longer be sufficiently suppressed.
This means the axion quality problem can remain in ordinary general relativity.
A New Possibility: Metric-Affine Gravity
Takeshita and Yoshioka investigated whether changing the theory of gravity could help.
Their work uses Metric-Affine Gravity (MAG).
In ordinary general relativity, the geometry of spacetime is mainly described using the metric. In MAG, however, the metric and the connection that describes how objects move through spacetime are treated as separate quantities.
This gives spacetime additional properties.
Two of the most important are torsion and non-metricity.
Torsion can be thought of as a twisting property of spacetime.
Non-metricity describes a situation where the usual rules for keeping distances and angles unchanged during parallel transport no longer hold.
These additional features allow MAG to contain gravitational terms that are not present in the usual formulation of general relativity.
Two important examples are the Holst term and the Nieh–Yan term.
These Extra Terms Can Strengthen the Wormhole
The researchers studied what happens when the axion-related scalar field is connected to these additional gravitational terms.
After solving for the independent connection in the theory, these interactions modify the equations that describe the wormhole.
A key factor, called G, changes the way the field behaves as one moves toward the wormhole's throat.
The important result is that these additional interactions can increase the wormhole action.
That is exactly what is needed to solve the axion quality problem.
Remember that the unwanted effect is suppressed by e⁻ˢ.
So if the action becomes larger, the symmetry-breaking effect becomes exponentially smaller.
In other words, the modified theory could make axionic wormholes much less dangerous to the axion.
Using Two Gravitational Effects Works Even Better
The researchers first studied different couplings individually.
When only the usual curvature of spacetime is coupled to the scalar field, their result agrees with previous work using the Palatini approach. In that case, sufficiently large coupling can help solve the axion quality problem.
They also studied the Nieh–Yan term and found that the problem can be alleviated when its effective coupling becomes sufficiently large.
The Holst term produces another interesting result. Its effect depends on the size of a quantity known as the Barbero–Immirzi parameter.
But the researchers did not stop with individual couplings.
They also studied combinations of two different terms.
They considered:
Curvature + Nieh–Yan
Curvature + Holst
Nieh–Yan + Holst
In all three cases, the range of parameters that can solve the axion quality problem becomes larger.
This means that combining different gravitational effects can provide more possibilities than using only one.
Could This Work With Cosmic Inflation?
There is another important question.
Even if the theory protects the axion, can it also describe the early universe correctly?
The researchers therefore investigated whether some of the same parameter regions could also support cosmic inflation.
They considered conditions corresponding to about 80 e-folds of inflation, a scalar spectral index between 0.97 and 0.98, and a tensor-to-scalar ratio below 0.038.
Their results identified representative regions where the requirements for suppressing axion symmetry breaking can overlap with conditions needed for successful inflation.
This is interesting because it means the same modified-gravity framework could potentially address problems involving both the axion and the early universe.
There Are Still Open Questions
The researchers also point out that their work does not completely solve every theoretical problem.
One important issue is perturbative unitarity.
The model requires some large non-minimal couplings. In theories with very large couplings, there can be an energy scale above which the theory may no longer provide reliable predictions.
The exact scale can depend on the gravitational theory, the background field and other parameters.
A complete study of this issue is therefore still needed.
What Could Come Next?
The idea could have implications beyond the strong CP problem.
Axions and related particles called axion-like particles (ALPs) are also possible candidates for dark matter.
Since wormholes can generate symmetry-breaking effects involving these particles, the mechanism studied in Metric-Affine Gravity could potentially be useful in future models of axion or ALP dark matter.
Researchers could next investigate the complete history of the universe, including inflation, reheating and dark matter production.
A New Way to Protect the Axion
The axion is an attractive solution to one of the deepest puzzles in particle physics, but quantum gravity creates a serious challenge.
Axionic wormholes could break the very symmetry that makes the axion solution work.
The new study suggests that a richer description of gravity may help protect the axion.
By allowing spacetime to have torsion and non-metricity, Metric-Affine Gravity introduces additional gravitational interactions through terms such as Holst and Nieh–Yan.
These interactions can increase the action of axionic wormholes. Because wormhole effects are exponentially suppressed by e⁻ˢ, even an increase in the action can make a huge difference.
The idea is still theoretical, and important questions remain unanswered. But the research offers an intriguing possibility:
Perhaps changing the geometry of gravity could help protect one of the most promising particles ever proposed to explain the mysteries of our universe.
Reference: Shonosuke Takeshita, Naoki Yoshioka, "Axionic Wormholes in Metric-Affine Gravity", Arxiv, 2026. https://arxiv.org/abs/2609.11010
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