University of California, Davis mathematicians have challenged the Lambda-cold dark matter model, publishing calculations in Proceedings of the Royal Society A that suggest Einstein’s equations naturally produce cosmic acceleration through a fundamental instability, potentially eliminating the need for mysterious dark energy to explain the expanding universe.
For nearly three decades, modern astrophysics has relied on dark energy to account for why the universe is not just expanding, but accelerating in that expansion. Now, a study from a team of mathematicians at the University of California, Davis, turns that assumption upside down by arguing that the math behind cosmic acceleration was sitting inside general relativity all along. The researchers examined the Einstein-Euler equations, which couple Einstein’s theory of gravity with the fluid dynamics governing matter in the cosmos. By testing the stability of these foundational equations, the authors found that the standard mathematical models used to reconstruct the evolution of the universe since the Big Bang harbor a deep structural weakness.
All the forces are in balance when a pencil is standing on end, so it is a ‘solution of the equations,’ but it’s unstable. Any breath of air and it falls away.
Blake Temple, corresponding author and professor emeritus of mathematics at UC Davis
To illustrate the mathematical problem, Blake Temple compared the standard model to a pencil balanced vertically on its tip. While theoretical forces balance in that state, the solution is exceptionally fragile. In physics, such delicate equilibria are typically categorized as unphysical because they are never observed in raw nature. The team’s analysis indicates that Friedmann spacetimes—the geometric framework underpinning conventional cosmic expansion models—suffer from this exact vulnerability at large length scales. Rather than smoothing out over time, minor disturbances in the matter-dominated universe grow progressively stronger, causing actual cosmic behavior to diverge sharply from standard predictions.
Investigating the Radiation Epoch and Radial Perturbations
The research did not set out to rewrite modern cosmology. According to the study’s corresponding author, the investigation initially began as an inquiry into whether a massive shockwave might account for early cosmic expansion, with the observed acceleration driven by an expanding wave trailing behind it. That line of inquiry led the team to uncover a family of self-similar solutions active during the radiation epoch of the Big Bang.
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. 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.
Blake Temple, corresponding author and professor emeritus of mathematics at UC Davis
When the researchers applied radial perturbations—disturbances changing with distance from a central symmetry point—to large length scales, the calculations proved definitive. The team demonstrated that Friedmann spacetimes are entirely unstable to these perturbations. This theoretical result challenges the Lambda-cold dark matter model as a viable, stable solution to the Einstein equations of general relativity, with or without the inclusion of dark energy.
Challenging the Copernican Principle and the Lambda-CDM Framework
The newly proposed mathematical structure implies that while the Big Bang should closely resemble a Friedmann spacetime near its center of symmetry, regions far from that center should exhibit distinct accelerations away from standard predictions. This spatial variation touches directly on the Copernican principle, the long-standing astronomical tenet named after Nicolaus Copernicus asserting that Earth occupies no privileged location in the universe.
The UC Davis researchers argue that both the standard Lambda-cold dark matter model and a spherically symmetric spacetime require a special point where observers must reside for the physics to remain plausible, meaning the principle must be applied with equal scrutiny to competing theories. Funding for the study was provided by the United Kingdom’s Engineering and Physical Sciences Research Council and the American Institute of Mathematics SQuaREs Program, though independent sources note that this theory remains speculative until validated by astronomical observations.