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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11 Comments
The solution is gravity waves from the singularity at the beginning of the universe. If the singularity is >3 dimensional, and in motion relative to our universe, we would be drawn after it as in the object vD23 discovered by Pieter van Dokkum in 2022. Since the singularity is moving at high velocity, our universe is not in danger of being swallowed up by it.
The episodic, or ‘bursty’ star development in the wake of vD23 is similar to the star development in the earliest galaxies, as well.
There is a much simpler and workable solution that offers a realistic explanation than dark energy and dark matter as influencing the oberved accelerating universe, galaxy spin dynamics and the cosmological “constant”. It even provides insight into the nature of gravity. The solution models a rotating universe, whereby the quantum nature of the virtual ubiquitous energy fields rotate within an expanding volume of spacetime. The Friedman universal expansion equations only model a flat non-rotating universal volume. When a rotational component replaces the static flat expansion part of the equation it provides a workable and natural solution for the cosmological constant, which in reality, is changing as the volume and diameter of spacetime increase as spacetime volume increases, all within Einstein’s general relativity equations. Basically, the model suggests cenrifugal force of a rotating universe is driving expansion, which explains redshift and observed universal acceleration. No need for dark energy. There is also a theoretical model that explains galaxy spin, whereby disk type galaxies act as a gravitational collective unit across a plane rather than a Newtonian discrete model of orbital mechanics.
goood
General Relativity and Quantum Mechanics are aberrations. Newtonian physics is the real science. Modify Newtonian physics to make it a complete theory. A Newtonian model where expansion is due to actual motion of bodies, a three-dimensional equivalent of planar elliptical motion, will not require any dark matter. The individual units of the universe just move away and return back along closed helical paths.
TRY this : The mathematical proof presented by mathematicians at UC Davis and University College London represents a critical, long-overdue paradigm shift. By demonstrating that the accelerating expansion of galaxies emerges naturally as an inherent geometric instability within the Einstein-Euler equations, this paper successfully exposes the standard Cosmological Constant ($\Lambda$) as an unnecessary mathematical patch.The fluid mechanics model correctly identifies the “shockwave” of spatial acceleration, but it can be significantly enhanced by anchoring it to the mechanical foundation of the Torsion Hill Framework. Your equations prove that flat Friedmann spacetime is as physically unstable as a balanced pencil; our framework solves this instability at the baseline by recognizing that pre-expansion space is an actively wound, high-torsion system.The localized compression core of this instability is dictated by our primary arithmetic origin (1 + 1 = -1 Effect ), scaling directly into the matrix composition of the spatial trough: (2D}+T) + (3D}+T}) = -1D+T Effect} Rather than letting the system collapse infinitely, the Torsion Hill model introduces a physical constraint via the Inversion Operator, where the absolute magnitude of this localized compression torque is converted directly into a positive, outward spatial expansion template:{V expansion} = frac{\Delta(3D}+T over (-1D+T Effect) x ( 1 – \frac{\text{m}}{\text{M}_{\infty}} Incorporating this mechanical uncoiling engine and its resulting spinning, helical trajectory ( Vh) provides your fluid equations with the concrete physical constraints, boundary parameters, and density caps required to perfectly calculate the real-time refresh rate of the universal matrix.
With expansion, space-time ‘stretches’ like the surface of an expanding balloon; this means space stretches (seen through larger distances between objects) and also time stretches (effectively speeds up).
There will be a logarithmic equation for the relationship between the size of the universe and the rate at which ‘background time’ passes (is. Time not measured in one specific location with its own gravitational relative effects).
Light behaves in regular ways, but it’s ‘speed’ is related to the rate of time; this means that although the behaviour of light may be constant, it’s speed will follow the relationship with the size of the universe (also affected by dense gravity in the early universe formation, forming an S shaped curve of expanding rate of time), with the speed being constant for any given era (ie. Light 3billion years ago all travels at the same speed because background time is the same at that point, but different to light 7bn ya or light now.
Time is on a logarithmic scale that we are trying to interpret as a linear progression, hence accelerated expansion is calculated in space, rather than a linear expansion of space coupled with an expansion of time.
The Dynamical Fourier Field (DFF) framework provides a compelling, mathematically rigorous alternative that completely replaces the need for dark matter particles. Operating as a simulated cosmology, the DFF framework resolves this by introducing the Residual Spectral Force (RSF).
Here is how the RSF elegantly resolves the dark matter problem without inventing new matter:
The Underlying Mechanism: The RSF is not a particle, but a long-range spectral coherence coupling between baryonic clusters. This force arises naturally from the global topology of the spectral manifold {K}.
Energy Density Match: The cosmological energy density of the RSF is \Omega_{RSF}=0.2621, which is numerically equivalent to the standard \Omega_{CDM}. However, rather than being hidden mass, it is the residual coherence energy of spectral phase correlations maintained across cosmic distances.
Observational Consistency: The RSF perfectly produces flat galaxy rotation curves and elegantly explains the observed lensing offset in the Bullet Cluster without the need for dark matter particles.
Solving the S_8 Tension: Furthermore, the RSF inherently resolves the S_8 tension without introducing new parameters. It predicts \sigma_8 = 0.75-0.78 through a Lorentzian power suppression.
It is time we transition from endlessly searching for invisible particles to understanding the geometric and spectral coherence of the universe itself.