Mathematicians Say the Universe May Not Need Dark Energy After All

A Three-Decade Consensus Under Pressure

For nearly thirty years, dark energy has served as the standard explanation for why the universe's expansion is speeding up. Now two independent lines of research are pushing back, arguing that the acceleration may emerge from the mathematics of cosmology itself, with no exotic energy needed.

An Instability in the Equations

A team of mathematicians — Christopher Alexander, Blake Temple, and Zeke Vogler — published a paper in Proceedings of the Royal Society A arguing that the standard Lambda-cold dark matter model rests on an unstable foundation. Reformulating the Einstein-Euler equations in self-similar variables, they showed that the critical Friedmann spacetime, the idealised uniformly expanding universe at the heart of standard cosmology, behaves as an "unstable saddle rest point." Any small perturbation, such as a region where matter density dips slightly below average, pushes the solution away from the Friedmann model into an accelerating expansion at intermediate times before decaying back. Crucially, the accelerations produced fall in the same range attributed to dark energy. The work builds on earlier research Temple co-authored with the late Joel Smoller.

A Cosmic Uncertainty Principle

Separately, theoretical physicist Savvas Koushiappas of Brown University proposes a different route to the same conclusion. He argues the universe may obey its own version of Heisenberg's uncertainty principle: its size and its rate of expansion cannot both be specified with perfect precision. When the scale factor and expansion rate are treated as quantum operators that do not commute, the resulting deformed Friedmann equation naturally produces late-time accelerated expansion without any dark energy term. The model also predicts the effective dark-energy equation of state should deviate slightly from a pure cosmological constant — a deviation that surveys like the Dark Energy Spectroscopic Instrument have already begun to hint at.

Testing the Alternatives

Both proposals face scrutiny. The Alexander-Temple-Vogler work operates in a simplified, pressureless and radially symmetric setting, leaving open whether the instability survives in a more realistic universe. Koushiappas's framework is a single-author theoretical paper that requires observational confirmation. Data from DESI, the Euclid mission, and the Vera C. Rubin Observatory in the coming years should help determine whether dark energy is a fundamental feature of the cosmos or, as these researchers suggest, a mathematical artefact of assumptions that were never quite right.