Topology may tame the cosmological constant, physicists report

Brown University physicists have proposed a way to explain why the universe is not expanding at the extreme rate predicted by quantum theory. Their study argues that the geometry of space-time, through a topological effect, may keep the cosmological constant stable despite quantum fluctuations.

The work, by Stephon Alexander, Heliudson Bernardo and Aaron Hui of the Brown Theoretical Physics Center, was published in Physical Review Letters, according to Brown University. The paper connects a proposed quantum gravity state with the quantum Hall effect, a well-tested phenomenon from condensed matter physics.

A long-running mismatch

The cosmological constant is the term associated with the energy driving the accelerating expansion of the universe. Brown University said the problem is that quantum field theory predicts empty space should contain fluctuations that add an enormous amount of vacuum energy, pushing the constant toward an extremely large value.

Astronomical observations show the constant is very small by comparison, Brown University said. If the predicted value were right, the universe would have expanded so quickly that galaxies, stars and planets would not have formed, according to the university’s summary of the research.

The term dates to Albert Einstein’s general relativity. Brown University said Einstein introduced it while trying to describe a static universe, then dropped it after Edwin Hubble’s 1929 discovery that the universe is expanding. Einstein later reportedly called the term his “biggest blunder.”

The constant returned to prominence after astronomers found in 1998 that cosmic expansion is accelerating. Brown University said that discovery made the cosmological constant useful again as an explanation for the acceleration, while sharpening the conflict with quantum field theory.

The quantum Hall link

Alexander and his colleagues studied the Chern-Simons-Kodama state, a proposed ground state in quantum gravity. Brown University said the team found that its mathematics resembles the structure behind the quantum Hall effect, in which electrical conductance takes exact values under very cold conditions and strong magnetic fields.

In the quantum Hall effect, those values stay fixed even when a material has imperfections. Brown University said that stability comes from topology, the mathematical study of properties tied to a system’s underlying shape or structure.

The researchers argue that a related topological protection may apply to the cosmological constant in the Chern-Simons-Kodama framework. “What we've shown is that if space-time has this non-trivial topology, then it resolves one of the deadliest problems of the cosmological constant,” Alexander said in Brown University’s announcement.

Alexander said quantum perturbations that would otherwise increase the cosmological constant become ineffective under this topology. Hui said the model suggests the cosmological constant, like conductance in the quantum Hall effect, can be restricted to certain allowed values for topological reasons.

Early step for quantum gravity

Brown University said physicists still do not have a complete quantum theory of gravity, and Alexander described the Chern-Simons-Kodama approach as a conservative route based on canonical quantization. He said the new work grew out of longstanding similarities he saw between that theory and the quantum Hall effect.

Alexander said more research is needed before the idea can be established as a full explanation of the cosmological constant problem. Brown University said the result also gives researchers a new reason to examine the Chern-Simons-Kodama state as a possible ingredient in a future theory of quantum gravity.

This story draws on original reporting from ScienceDaily.