Dark energy and universe expansion concept illustration in space.

Богдан Скрипник

New Theory Suggests the Universe’s Accelerating Expansion Was Built Into the Big Bang All Along

In A Nutshell

  • Scientists have long relied on a mysterious force called dark energy to explain why the universe is expanding faster and faster, but it has never been directly detected.
  • A new mathematical study argues that the standard equations describing the universe contain an instability that nobody had fully accounted for.
  • A small disturbance at the moment of the Big Bang could naturally produce the kind of accelerating expansion dark energy was invented to explain.
  • The acceleration in this model is temporary, not eternal, and the study is a mathematical proof, not an observational confirmation that dark energy is unnecessary.

For decades, scientists have plugged a mysterious, invisible force called dark energy into their equations to explain one of cosmology’s biggest puzzles: why the universe appears to be expanding faster and faster. Dark energy has never been directly detected, has no known connection to any other area of physics, and requires roughly 70% of the universe’s total energy to consist of something no one can identify. Now, a new mathematical study proposes that, at least in principle, some cosmic acceleration may arise from Einstein’s equations themselves, without adding dark energy.

Published in Proceedings of the Royal Society A, the research argues that the standard mathematical framework describing how the universe expands has an instability nobody had fully accounted for. A tiny nudge at the moment of the Big Bang, the authors contend, is enough to send the universe drifting away from the smooth picture those equations describe.

That matters because of a problem that has nagged cosmologists since 1999, when supernova data revealed that galaxies appear to be flying apart at an increasing rate rather than slowing down. To make sense of that, physicists reintroduced a term Einstein himself had famously called “the greatest blunder of my career,” the cosmological constant, now reinterpreted as dark energy. Squaring that data with the standard model requires roughly 70% of the universe’s energy density to consist of this anti-gravitating force. The new study asks whether that fix was ever necessary.

A Wobble Built Into the Standard Cosmic Model

In the early 1920s, a Russian mathematician named Alexander Friedmann solved Einstein’s field equations and found a family of solutions describing a universe that expands from an initial point. Those solutions became the mathematical foundation of the Big Bang theory and remain central to cosmology today. One special version, with perfectly flat geometry, has been the favored model for decades, supported by measurements of faint microwave radiation left over from the early universe.

According to the new paper, this perfectly flat standard model is what mathematicians call an unstable saddle point. A ball balanced on top of a hill is technically a valid position, but the slightest push sends it tumbling. Working through the mathematics, the authors prove that all versions of this standard model are unstable to small disturbances at or near the Big Bang, meaning the smooth, perfectly uniform universe those equations describe is not a state the real universe is obligated to stay in.

dark energy infographic
Could the Big Bang itself explain why the universe keeps speeding up? A new mathematical study says maybe. (Image by StudyFinds)

Einstein’s Equations, No Dark Energy Added, Produce Cosmic Acceleration

Rather than pointing a telescope at the sky, the researchers did their work entirely on paper, reformulating Einstein’s equations in a way that let them treat the standard cosmic model as a fixed point in a mathematical system, then probe what happens when conditions near the Big Bang deviate slightly from perfect. It is the same basic logic as asking whether a pendulum, given a small push, will swing back to center or keep moving away.

At every level of their analysis, the standard model fails that test. When the researchers zeroed in on a class of solutions where matter density near the Big Bang is slightly lower than the standard model predicts, those solutions accelerated away from it, which is precisely the kind of behavior dark energy was introduced to explain.

How the Big Bang’s Instability Drives Cosmic Speed-Up

Crucially, that acceleration does not last forever. In the scenarios the authors analyze, the expansion eventually settles back toward the same baseline model it started from. The acceleration is real, but temporary, a consequence of instability baked into the Big Bang rather than an eternal force permeating all of space.

As the authors write, “instabilities inherent in the Einstein-Euler equations,” the combined mathematical framework governing gravity and matter, provide “a natural mechanism for an accelerated expansion without recourse to a cosmological constant or dark energy.” Einstein’s original equations, without modifications, may already contain the seeds of what astronomers are observing.

That said, the theory comes with an uncomfortable implication. Accelerations of the kind the authors describe have a center of expansion, which sits uneasily next to the longstanding assumption in cosmology that Earth is not in a special cosmic location. The authors note that all current models appear to place Earth in some sort of special position and suggest some tension with that assumption may simply be unavoidable, though this remains a point for debate.

A Math Proof, Not a Verdict on Dark Energy

Quantitatively matching this mechanism to the observed acceleration of galaxies remains a goal for future work, and the current standard model, which includes dark energy, still accounts for most cosmological data. But proving that the Big Bang itself seeds an instability capable of mimicking cosmic acceleration is a notable result on its own. If future work shows the mechanism holds up against observations, it could reopen one of cosmology’s biggest questions: whether the effect now attributed to dark energy might instead reflect something that was always hiding inside the Big Bang.


Paper Notes

Limitations

This study is a mathematical analysis, not an observational or experimental one. The authors restrict their analysis to pressureless, matter-dominated solutions and note that the global dynamics for overdense perturbations will be addressed in a subsequent paper. The paper focuses on what the authors call the “asymptotic analysis” and states that the “existence theory,” establishing conditions under which the formal mathematical solutions correspond to exact physical solutions, will also be addressed in future publications. The authors explicitly acknowledge that directly comparing their proposed acceleration mechanism to observed supernova data remains an open task.

Funding and Disclosures

C. Alexander gratefully acknowledges the support of the EPSRC project no. EP/S02218X/1 and the ERC starting grant no. 101078061 SINGinGR, under the European Union’s Horizon Europe program for research and innovation. This research was also supported by the American Institute of Mathematics SQuaRE Program. The authors declare no competing interests and state that no AI-assisted technologies were used in creating the article.

Publication Details

Authors: C. Alexander (Department of Mathematics, University College London, London, UK); B. Temple and Z. Vogler (Department of Mathematics, University of California, Davis, CA, USA). The paper is dedicated to the authors’ former collaborator Joel Smoller, who died shortly before publication of an earlier related work. | Journal: Proceedings of the Royal Society A | Paper title: “The instability of critical and underdense Friedmann spacetimes at the Big Bang as an alternative to dark energy” | DOI: https://doi.org/10.1098/rspa.2025.0912 | Published: Proc. R. Soc. A 482: 20250912 (2026)

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