The cosmological constant is the mathematical description of the energy driving the ever-accelerating expansion of the cosmos. Quantum field theory (QFT), the leading theory describing elementary particles and forces, predicts that quantum fluctuations in the vacuum of space should make the constant's value enormous - practically infinite. Yet its observed value is a tiny fraction of that prediction.
The Brown team shows that the math underlying the simplest formulation of quantum gravity bears a striking resemblance to the math describing the quantum Hall effect, an exotic state of matter in which electricity flows with uncanny precision. In the quantum Hall state, electrical conductance is held steady regardless of any imperfections in the conducting material, due to the system's topology - the mathematical shape of the quantum state. The researchers found an analogous topology in what is known as the Chern-Simons-Kodama state, a proposed ground state of quantum gravity.
"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," said study co-author Stephon Alexander, a professor of physics at Brown. "All the quantum perturbations that should blow up the value of the cosmological constant are rendered inert by this topology, which keeps the constant's value stable."
The research, co-authored with Brown Theoretical Physics Center colleagues Aaron Hui and Heliudson Bernardo, is published in Physical Review Letters.
The cosmological constant first appeared in Einstein's equations for general relativity as a stabilizing term representing a repulsive force in the vacuum of space. Following Edwin Hubble's 1929 discovery that the universe was expanding, Einstein removed the term - famously calling it his "biggest blunder." The constant was reinstated in 1998 when scientists discovered the universe's expansion is accelerating.
Alexander had been aware of mathematical similarities between the Chern-Simons-Kodama state and the quantum Hall effect, but turned to Hui, an assistant professor specializing in topological systems, to work out the implications. Together they showed that the cosmological constant has a similar topological protection in the CSK state as electrical conductance has in the quantum Hall effect.
"What we find is that this quantization of the electrical conductance in quantum Hall has an analog with the cosmological constant," Hui said. "It also ends up becoming quantized for topological reasons. There turn out to be constraints in the theory that force the cosmological constant to take certain allowed quantized values."
Alexander acknowledges there is much more work to be done to fully flesh out a topological solution to the cosmological constant problem, but finding a potential solution to the gravitational aspect is a crucial start. The work also bolsters the profile of the Chern-Simons-Kodama state as a candidate for a long-sought theory of quantum gravity.
"We took something old, which is this conservative, canonical approach to quantum gravity, and discovered something new that had been there all along," Alexander said. "Now we're working on a bigger picture of how this phenomenon works."
Research Report:Cosmological Constant from Quantum Gravitational Theta Vacua and the Gravitational Hall Effect
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