Mathematicians challenge dark energy theory in new study

Mathematicians at the University of California, Davis, argue that the prevailing Lambda-cold dark matter (Lambda-CDM) model may not be a viable stable solution of Einstein's equations, potentially offering an alternative explanation for the universe's accelerating expansion without invoking dark energy.

The study, whose corresponding author is Blake Temple, a distinguished professor emeritus of mathematics at UC Davis, examined the Einstein-Euler equations, which combine general relativity with fluid dynamics to model cosmic behavior. The researchers found that Friedmann spacetimes, which form the foundation of conventional models of cosmic expansion, are unstable at both small and large scales in the context of the Big Bang.

Dark energy has been the leading explanation for cosmic acceleration since astronomers discovered in the 1990s that the universe's expansion was speeding up. The concept traces back to Einstein's cosmological constant, which he introduced to make his equations accommodate a static universe and later called his "biggest blunder" after Edwin Hubble found evidence of expansion. The constant was revived decades later to account for the observed acceleration.

Temple compared the standard solution 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."

He argued that such unstable solutions are not physically realistic. "Unstable solutions in physics and science are considered not physical," Temple said. "You'll never observe them in nature."

The researchers' analysis suggests that the instability of Friedmann spacetimes could naturally drive accelerated expansion. "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.

The study began with a different hypothesis. "Our first idea was that maybe the universe was expanding because there was a shockwave, and the anomalous acceleration was the expanding wave behind that shockwave," Temple said. The researchers then identified self-similar solutions, patterns that retain their structure across scales, associated with the radiation-dominated period of the early universe.

The mathematical results indicate that the standard model is vulnerable to disturbances that grow rather than fade. "We prove that, like Einstein's static model, the Friedmann spacetimes are all unstable to radial perturbation at large length scales," Temple said. "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."

"This means," he added, "that the Big Bang should generically look exactly like a Friedmann spacetime near the center of symmetry, but generically one should observe accelerations away from Friedmann far from the center."

The alternative model introduces a center of spherical symmetry, raising questions about the Copernican principle, which holds that Earth's location is not special. Temple argued that both models require a special location. "Both the Lambda-cold dark matter model and a spherically symmetric spacetime produce a special place where we must lie for the model to be physically plausible," he said. "If this principle rules out one, it has to rule out the other."

The findings represent a theoretical challenge rather than observational proof that dark energy is unnecessary. Determining whether this alternative can describe the actual universe would require comparing its predictions with astronomical observations.

The research received funding from the United Kingdom's Engineering and Physical Sciences Research Council and the American Institute of Mathematics SQuaREs Program.