One of the biggest unsolved problems in physics centers around a number known as the cosmological constant. This value represents the energy responsible for the accelerating expansion of the universe. It is also at the center of a major conflict between two of science’s most successful theories.
According to quantum field theory (QFT), a framework that describes elementary particles and their interactions, empty space should be filled with quantum fluctuations that yield enormous amounts of energy. In fact, calculations show that the cosmological constant should be so large that it virtually approaches infinity.
But if you look, you’ll see something completely different. The actual value of the cosmological constant is incredibly small compared to what theory predicts.
Now, researchers at Brown University have proposed a possible explanation.
Their work suggests that mathematical features of spacetime itself may prevent the cosmological constant from expanding to the huge values expected from quantum physics. The idea exploits an unexpected connection between quantum gravity and the quantum Hall effect, a remarkable phenomenon in condensed matter physics.
Surprising link between quantum gravity and quantum Hall effect
The researchers found that the mathematics behind their simple approach to quantum gravity is very similar to the mathematics that describes the quantum Hall effect, an unusual state of matter in which electrical conductivity takes on very precise values.
In the quantum Hall effect, these values remain fixed even if the conducting material contains defects. Stability comes from topology, a branch of mathematics concerned with the underlying “shape” or structure of a system.
The researchers claim that a similar type of topology appears in the Chern-Simmons-Kodama state, which has been proposed as the ground state of quantum gravity.
“What we have shown is that when spacetime has such a nontrivial topology, one of the most critical problems about the cosmological constant is solved,” said study co-author Stephon Alexander, a professor of physics at Brown University. “Any quantum perturbations that would blow up the value of the cosmological constant are inactivated by this topology, keeping the value of the constant stable.”
The study was co-authored by Alexander and colleagues at the Brown Center for Theoretical Physics, Aaron Hoy and Heliudson Bernardo. physical review letter.
Einstein’s “ugly” cosmological constant
The cosmological constant first appeared in Albert Einstein’s general theory of relativity, a theory of space, time, and gravity.
At the time, Einstein believed that the universe was stationary. To prevent his equations from predicting the collapse of the universe, he introduced the cosmological constant as a kind of repulsive effect in empty space that offsets gravity.
After Edwin Hubble discovered in 1929 that the universe was expanding, the idea seemed unnecessary. After all, the universe was not static, so Einstein removed this term from the equation. He reportedly disliked this constant and later called it his “greatest failure.”
For decades, the cosmological constant faded into obscurity.
Then, in 1998, astronomers made a surprising discovery. That means the expansion of the universe is accelerating. Rather than disappearing from the story, the cosmological constant suddenly became essential again because it could potentially explain this accelerating expansion.
Cosmological constant problem
The return of the cosmological constant has caused serious problems.
In the years that constants fell out of favor, quantum field theory became one of the most successful theories in science and became the basis of the Standard Model of particle physics.
QFT describes empty space as non-empty. Instead, it is filled with particles that constantly appear and disappear due to quantum fluctuations.
All this activity should contribute enormous amounts of vacuum energy. That vacuum energy is related to the cosmological constant, which means the constant must be very large.
But observations show that this is not the case.
If the cosmological constant were as large as predicted by QFT, the universe would have expanded rapidly and galaxies, stars, planets, and ultimately life would never have formed.
The discrepancy between theory and observation remains one of the most complex problems in modern physics. This puzzle becomes even more impressive because the extraordinary precision of quantum field theory has been repeatedly confirmed experimentally in other situations.
topological solution
Alexander has spent years researching Chern-Simmons-Kodama (CSK) theory, a proposal for quantum gravitational states generated from quantum field theory.
Physicists do not yet have a complete quantum theory of gravity that explains gravity at the smallest scales. According to Alexander, the CSK approach is one of the easier possibilities.
“This is a very conservative approach to quantizing gravity,” he says. “This is the approach that people like Dirac, Schrödinger, and Wheeler use. It’s just good old-fashioned quantization.”
Alexander had long noticed similarities between CSK theory and the mathematics of the quantum Hall effect. To better understand these relationships, he collaborated with Hui, an assistant professor at Brown University who studies topological systems.
“This is the beauty of the Brown Center for Theoretical Physics,” Alexander said. “We want to be a place where many perspectives come together, and this is where we practice what we preach: cosmologists working closely with condensed matter theorists.”
How topology creates stability
The researchers found that the cosmological constant in the CSK framework appears to benefit from the same kind of topological protection seen in the quantum Hall effect.
The quantum Hall effect occurs when electricity flows through a very thin material that is exposed to a magnetic field.
Imagine a thin rectangular metal strip through which an electric current flows. When a magnetic field is applied, a second voltage is generated at right angles to the current. This effect produces a voltage known as the Hall voltage (named after Edwin Hall, who discovered the Hall voltage).
Under normal conditions, the Hall voltage changes smoothly as the magnetic field increases.
However, at extremely low temperatures and very strong magnetic fields, the behavior changes dramatically. The Hall voltage does not change smoothly, but increases with distinct steps and plateaus. Remarkably, these values remain the same regardless of the material used and the defects it contains.
Its reliability comes from its topology.
In such extreme states, electrons behave collectively and enter highly correlated quantum states. The topology of the state fixes the step and plateau values, making it tolerant to disturbances and defects.
The Brown researchers argue that a similar process occurs in the CSK description of quantum gravity.
Just as topology locks the Hall voltage to a particular value, the topology of spacetime can lock the cosmological constant to a stable value and protect it from quantum fluctuations that would make it much higher.
“What we discovered is that the quantization of the electrical conductance of quantum holes is similar to the cosmological constant,” Hui said. “Also, it ends up being quantized for topological reasons. It turns out that there are constraints in the theory that force the cosmological constant to take on a certain allowed quantization value.”
New direction of quantum gravity
Alexander emphasizes that much more research is needed before a topological explanation of the cosmological constant is fully established.
Still, he believes the discovery is an important step toward solving the gravitational side of the problem. The study also strengthens the case that CSK states are strong candidates for future theories of quantum gravity.
“We took something old, a conservative, standard approach to quantum gravity, and discovered something new that had always been there,” Alexander said. “We are now working to understand the bigger picture of how this phenomenon works.”
