New mathematical research suggests dark energy may not be needed to explain the accelerating expansion of the universe, challenging the foundations of the standard cosmological model.
Mathematicians are questioning whether dark energy is actually responsible for the universe’s accelerating expansion.
In a new study published in Proceedings of the Royal Society A, researchers at the University of California, Davis present mathematical evidence that instabilities within the Einstein-Euler equations suggest the current model of the expanding universe may not be viable. The Einstein-Euler equations combine general relativity and fluid dynamics and are widely used to model galaxies, black holes, and the expansion of the cosmos.
The findings directly challenge the Lambda-cold dark matter model, the leading Big Bang cosmology framework.
Study corresponding author Blake Temple, distinguished professor emeritus of mathematics at UC Davis, compared the standard cosmological model 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.”
Friedmann Spacetime Instability Challenges Dark Energy
According to Temple, the team’s calculations show that Friedmann spacetimes, the mathematical models used to describe cosmic expansion, are unstable at both small and large scales near the Big Bang. He said this makes them the most unstable solutions of all.
“Unstable solutions in physics and science are considered not physical,” Temple said. “You’ll never observe them in nature.”
Temple said this instability points to a simpler explanation that remains entirely within Einstein’s original theory of gravity.
“The instability of all Friedmann spacetimes to accelerated expansion suggests a simpler, more natural explanation for the acceleration of the universe than dark energy,” he said.
Why the Cosmological Constant Returned
Dark energy was proposed nearly 30 years ago as a way to explain why the universe’s expansion appears to be speeding up.
The concept traces back to Einstein’s 1915 equations of general relativity. To create a static universe, Einstein added an antigravity term known as the cosmological constant. After Edwin Hubble discovered in 1929 that the universe was expanding, Einstein reportedly referred to the cosmological constant as his “biggest blunder” because, without it, his equations would have predicted expansion.
In the 1990s, however, the cosmological constant was revived and linked to dark energy as a possible explanation for accelerating expansion. Modern cosmological models are built on the concept of a “Friedmann universe,” in which matter expands while remaining evenly distributed throughout space at any given time.
Searching for an Alternative Explanation
Temple and his colleagues believed there were mathematical problems with this picture, prompting them to investigate other possible causes of cosmic acceleration.
“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. “Then we realized there’s a family of self-similar solutions during the radiation epoch of the Big Bang, which might model that expanding wave.”
Self-similar equations describe systems that preserve the same overall pattern or structure across different scales.
Self-Similar Equations Reveal Instability
In the new study, the researchers used a self-similar version of Einstein’s equations developed in earlier work to represent the standard cosmological model as a rest point of the equations. This approach allowed them to fully analyze the model’s stability and, more broadly, the stability of all Friedmann spacetimes during the matter-dominated era of the Big Bang.
“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.”
Cosmic Acceleration Without Dark Energy
The researchers concluded that the universe’s accelerating expansion emerges naturally from the Einstein-Euler equations and does not require either a cosmological constant or dark energy.
Their findings also challenge the Copernican principle, the idea that Earth does not occupy a special location in the universe.
“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,” Temple said. “If this principle rules out one, it has to rule out the other.”
Reference: “The instability of critical and underdense Friedmann spacetimes at the Big Bang as an alternative to dark energy” by Christopher Alexander, Blake K. Temple and Zeke Vogler, 27 May 2026, Proceedings of the Royal Society A: Mathematical Physical and Engineering Science.
DOI:10.1098/rspa.2025.0912
The study was funded by the United Kingdom’s Engineering and Physical Sciences Research Council and the American Institute of Mathematics SQuaREs Program.
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