Mathematicians at the University of California, Davis published research in Proceedings of the Royal Society A arguing that Einstein's equations may naturally produce cosmic acceleration without requiring dark energy.
The team, led by Blake Temple, a distinguished professor emeritus of mathematics at UC Davis, analyzed the Einstein-Euler equations, which combine general relativity with fluid dynamics. Their calculations reveal that Friedmann spacetimes, the mathematical foundation of standard cosmological models, are unstable at both small and large scales.
Temple compared the instability to a pencil balanced on its tip. "All the forces are in balance when a pencil is standing on end, so it is a 'solution of the equations,'" he said. "But it's unstable. Any breath of air and it falls away."
The researchers used self-similar solutions of Einstein's equations to model how the universe might behave after small disturbances. Their analysis suggests that the universe could depart from standard predictions far from a central point while resembling the Friedmann model nearby.
"The instability of all Friedmann spacetimes to accelerated expansion suggests a simpler, more natural explanation for the acceleration of the universe than dark energy," Temple said. He added, "This appears to rule out the Lambda-cold dark matter model as a viable stable solution of the Einstein equations of general relativity, with or without dark energy."
The findings present a theoretical challenge to standard cosmology rather than observational proof. Determining whether this alternative can describe the actual universe would require comparing its predictions to astronomical observations.
The study also raises questions about the Copernican principle, which holds that Earth's location is not fundamentally special in the universe.