Mathematicians from University College London and the University of California, Davis, have unveiled a groundbreaking mathematical proof demonstrating that the accelerating expansion of the universe can be explained without dark energy. This finding poses a significant challenge to the lambda cold dark matter model, the predominant cosmological framework that has prevailed for nearly three decades.
C. Alexander and collaborators provide proof that the inherent instability of the Einstein-Euler equation renders current expanding universe models infeasible. Image credit: M. Weiss / Harvard-Smithsonian Center for Astrophysics.
Nearly 30 years ago, dark energy was proposed as the force driving the accelerating expansion of the universe.
This concept mirrors Albert Einstein’s 1915 gravity equation within his general relativity framework.
To create a static universe, Einstein initially introduced an antigravitational factor, known as the cosmological constant.
After Edwin Hubble’s discovery in 1929 of the universe’s expansion, Einstein famously deemed the cosmological constant his “greatest failure” as it was unnecessary for predicting the expansion.
However, in the 1990s, the cosmological constant concept was revived to explain the universe’s accelerating expansion linked to dark energy.
Blake Temple, a professor at the University of California, Davis, stated, “The Friedman family of spacetime has served as a cornerstone of contemporary cosmology since Lemaître and Hubble first articulated the theory of an expanding universe stemming from an early Big Bang singularity.”
This theory is grounded in a specific solution to Einstein’s field equations discovered by Alexander Friedman in the early 1920s.
Friedman initially sent his solution to Einstein in 1922, who dismissed it, believing the universe to be static. However, following Friedman’s appeal, the solution gained acceptance.
By 1931, Einstein recognized that static models were unstable, acknowledging Hubble’s 1929 findings of an expanding universe, and praising Lemaître’s cosmology based on Friedmann spacetime as the most elegant explanation of creation.
Temple and his co-authors propose a theorem suggesting that all Friedmann spacetimes are unstable to any form of radial perturbations.
“At first, we considered that the universe’s acceleration might be due to a shock wave, with the anomalous acceleration resulting from an expansion wave following that shock,” Professor Temple noted.
“Later, we realized that during the radiation epoch of the Big Bang, there existed self-similar solutions that could model an expanding wave.”
Self-similar equations depict phenomena that retain their structure regardless of scale.
In their paper, the mathematicians utilize a self-similar version of the Einstein equations, previously derived, to characterize the Standard Model of cosmology as the stationary point of their equations.
This establishes a comprehensive mathematical framework for assessing the stability of the Standard Model and, more broadly, the stability of all Friedmann spacetimes in the matter-dominated epoch of the Big Bang.
“We demonstrated that, akin to Einstein’s static model, all Friedmann spacetimes are unstable to radial perturbations on large scales,” Professor Temple affirmed.
“This finding largely discounts the lambda cold dark matter model, with or without dark energy, as a stable solution to Einstein’s equations of general relativity.”
“In essence, the Big Bang should resemble Friedmann spacetime near the center of symmetry, while we should observe an acceleration away from Friedmann further from the center.”
Recent research indicates that the accelerating universe expansion is a direct result of the Einstein-Euler equation, without requiring a cosmological constant or dark energy.
This mathematics raises questions about the Copernican principle, which posits that Earth’s position is not special within the universe.
“Both the lambda cold dark matter model and spherically symmetric spacetime demand that the model occupies a specific position to remain physically valid,” Professor Temple explained.
“If this principle excludes one model, it must also exclude the other.”
Visit the research paper published in this week’s Proceedings of the Royal Society A.
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C. Alexander et al. 2026. The instability of critical and crowded Friedmann spacetime in the Big Bang as an alternative to dark energy. Proceedings A 482 (2338): 20250912; doi: 10.1098/rspa.2025.0912
Source: www.sci.news
