Mathematicians at the University of California, Davis, have proposed a challenge to the widely accepted explanation that dark energy is driving the accelerating expansion of the universe. In a study published in Proceedings of the Royal Society A, their calculations suggest that acceleration could arise naturally from Einstein’s equations because the standard mathematical description of an expanding universe may be fundamentally unstable. The result is a theoretical challenge, not observational proof that dark energy is unnecessary.
A possible instability in the standard cosmological model
The study examines the lambda cold dark matter model, or ΛCDM, the main framework scientists use to describe the universe’s evolution since the Big Bang. The researchers studied the Einstein-Euler equations, which combine Einstein’s general theory of relativity with equations describing the behavior of fluids. Together, these equations can be used to investigate systems ranging from galaxies and black holes to the expansion of the universe.
Blake Temple, the study’s corresponding author and a distinguished professor emeritus of mathematics at the University of California, Davis, compares the proposed instability with balancing a pencil vertically on its tip.
“When the pencil stands on end, all the forces are balanced, so it becomes a ‘solution to the equation,’” he said. “But it’s unstable. If you breathe in air, it will fall off.”
Temple said the team’s mathematical analysis shows that Friedmann spacetime—the basis of traditional models of cosmic expansion—is unstable on both small and large scales in the context of the Big Bang. In his view, the standard solutions are highly unstable.
“Unstable solutions in physics and science are considered non-physical,” Temple said. “You would never observe it in nature.”
If the universe evolves naturally in a way that reflects this instability, another form of energy might not be needed to explain its accelerating expansion. Instead, the explanation could be contained within Einstein’s original theory of gravity.
“The instability of all Friedmann spacetimes with respect to accelerating expansion suggests a simpler and more natural explanation for the acceleration of the universe than dark energy,” Temple said.
Why dark energy is the standard explanation
For nearly 30 years, dark energy has been the leading explanation for one of astronomy’s most puzzling observations: the universe is expanding, and that expansion is accelerating.
The idea is connected to Einstein’s 1915 theory of general relativity, which describes gravity as the curvature of space and time. Einstein initially believed the universe was static rather than expanding or contracting. To make his equations consistent with that assumption, he introduced a mathematical term to counteract gravity: the cosmological constant.
That picture changed in 1929, when Edwin Hubble found evidence that the universe was expanding. Einstein later reportedly called the introduction of the cosmological constant his “greatest failure,” because the original equations without the additional term could have predicted an expanding universe.
The cosmological constant gained renewed attention in the 1990s, when astronomers discovered that cosmic expansion was accelerating. It became closely associated with dark energy, the name given to the unknown component believed to be responsible for that acceleration.
Today’s standard cosmological framework is based on the Friedmann universe, a mathematical description in which space expands while matter is distributed evenly throughout the universe at any given time. This large-scale assumption of uniformity plays a central role in reconstructing the universe’s history.
Temple and his collaborators questioned whether the mathematics underlying this description could remain stable, leading them to investigate alternative explanations for the observed acceleration.
How Einstein’s equations could produce acceleration
The researchers initially considered whether enormous shock waves might help explain the expansion of the universe and its unexpected acceleration.
“Our first thought was that the universe was expanding, perhaps because of a shock wave, and that the anomalous acceleration was an expansion wave behind that shock wave,” Temple said. “Then we realized that in the radiation epoch of the Big Bang, there existed a series of self-similar solutions that could potentially model that expanding wave.”
In mathematics and physics, a self-similar solution retains the same underlying structure when viewed at different scales. Fractals provide a familiar example: similar shapes appear repeatedly as the pattern becomes larger or smaller.
The researchers identified a family of self-similar solutions associated with the radiation-dominated period of the early universe, when radiation played a major role in determining cosmic evolution.
Building on previous work, they used the self-similar form of Einstein’s equations to represent the standard cosmological model as a stationary point—a mathematical state in which the variables defining a system do not change. This allowed them to examine whether small deviations from that state would fade over time or grow.
The analysis provided a framework for assessing the stability of the Standard Model and, more broadly, Friedmann spacetime during the matter-dominated epoch of the early universe, when matter became more influential than radiation.
A theoretical challenge to ΛCDM
The results suggest that traditional mathematical descriptions of an expanding universe may be vulnerable to disturbances that grow rather than disappear.
“We have shown that, like Einstein’s static model, all Friedmann spacetimes are unstable to radial perturbations on large length scales,” Temple said. “This seems to rule out the lambda cold dark matter model, with or without dark energy, as a viable stable solution to the Einstein equations of general relativity.”
A radial perturbation is a disturbance that changes with distance from a central point. In the researchers’ framework, such disturbances could cause the universe’s expansion to diverge from the predictions of the standard Friedmann model.
“This means that in general the Big Bang should look exactly like Friedmann spacetime near the center of symmetry, but in general we should observe an acceleration away from Friedmann far from the center,” Temple added.
In other words, the universe could behave much as the Standard Model predicts near its central region but expand differently at greater distances.
The researchers argue that this instability could provide a natural mechanism for accelerating cosmic expansion without adding to the cosmological constant or invoking dark energy. Their calculations show that acceleration can emerge directly from the Einstein-Euler equation itself.
However, the work does not demonstrate through observations that dark energy is unnecessary. Further theoretical and observational studies will be needed to determine whether the proposed model makes predictions that match astronomical measurements.
Would the model imply a special location?
The research also raises broader questions about the Copernican principle. Named after astronomer Nicolaus Copernicus, whose work helped overturn the belief that Earth occupies the center of the solar system, the principle holds that our location in the universe is not fundamentally special or privileged.
The assumption is central to modern cosmology and supports the view that the universe should look broadly similar to observers in different locations when examined on sufficiently large scales.
The researchers’ alternative mathematical framework introduces a center of spherical symmetry. This raises the question of where an observer would need to be located for the model to agree with observations.
Temple argues that the Copernican principle must be applied consistently when competing explanations are evaluated.
“Both the lambda cold dark matter model and spherically symmetric spacetime create a special place where the model has to lie in order to be physically valid,” Temple said. “If this principle excludes one, it must also exclude the other.”
The research opens another avenue for investigating why the universe’s expansion is accelerating. Dark energy remains a central component of prevailing cosmological models, but the researchers argue that general relativity’s mathematics could offer a different explanation for the same phenomenon.
If additional theoretical and observational studies support their interpretation, the work could prompt a reassessment of how scientists understand cosmic expansion and the mathematical foundations of the Big Bang.
The research was funded by the UK Engineering and Physical Sciences Research Council and the American Institute of Mathematics SQuaREs programme.
Source: www.sciencedaily.com
