Researchers at the University of California, Davis, have presented a mathematical challenge to the widely accepted idea that dark energy is responsible for the accelerating expansion of the universe. In a study published in Proceedings of the Royal Society A, they argue that instabilities in the standard mathematical description of cosmic expansion could allow acceleration to arise directly from Einstein’s equations, without requiring an additional form of energy. The work is a theoretical result, not observational evidence that dark energy does not exist.
An instability in the standard cosmological model
The study examines the lambda cold dark matter model, or ΛCDM, which is the main framework scientists use to describe the universe’s evolution since the Big Bang. The researchers analyzed the Einstein-Euler equations, which combine general relativity with equations describing the behavior of fluids. These mathematical tools can be used to study 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, compared the issue to 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.”
According to Temple, the team’s analysis indicates 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. The researchers say that 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 developed naturally in accordance with the behavior predicted by these models, the instability could offer another explanation for its accelerating expansion. In that case, an additional form of energy might not be necessary because the effect could already be contained in Einstein’s 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 became the leading explanation
For almost 30 years, dark energy has been the leading explanation for the discovery that the universe is not only expanding but expanding at an increasing rate.
The concept is connected to Albert Einstein’s 1915 theory of general relativity, which describes gravity as the curvature of space and time. Einstein initially assumed that the universe was static, neither expanding nor contracting. To make his equations consistent with that assumption, he introduced a term that counteracted gravity: the cosmological constant.
That view changed after Edwin Hubble found evidence in 1929 that the universe was expanding. Einstein later famously described introducing the cosmological constant as his “greatest failure,” because the original equations without the additional term could have predicted an expanding universe.
The cosmological constant regained 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 thought to drive that acceleration.
Modern cosmology is based in part on the Friedmann universe, a mathematical description in which space expands while matter is distributed uniformly across the universe at any given time. This assumption of large-scale uniformity is central to reconstructing the history of the cosmos.
Temple and his collaborators questioned whether the mathematics underlying this description could remain stable. Their work explores whether the observed acceleration might instead emerge from the equations used to describe gravity and matter.
Self-similar solutions and cosmic expansion
The researchers initially considered whether enormous shock waves could account for the universe’s expansion 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.”
Self-similar solutions are patterns that retain the same underlying structure when viewed at different scales. Fractals provide a familiar example: their shapes repeat as they are enlarged or reduced.
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 earlier work, they used the self-similar form of Einstein’s equations to represent the standard cosmological model as a stationary point. In mathematics, a stationary point is a state in which the variables defining a system do not change. The approach allowed the researchers to examine whether small deviations from that state would fade away or grow over time.
The analysis provided a framework for assessing the stability of the Standard Model and, more broadly, Friedmann spacetime during the matter-dominated period of the early universe, when matter became more influential than radiation.
A challenge to the standard Big Bang model
The results suggest that conventional 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’ mathematical framework, such a disturbance could cause the universe’s behavior to depart 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 practical terms, the model suggests that 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 modifying the cosmological constant or introducing dark energy. Their calculations indicate that acceleration can emerge directly from the Einstein-Euler equation.
However, the finding is a theoretical challenge to standard cosmology, not observational proof that dark energy is unnecessary. Determining whether the alternative model describes the real universe will require comparing its predictions with astronomical observations.
Does the model imply a special location?
The research also raises questions about the Copernican principle, which holds that Earth and its observers do not occupy a fundamentally special or privileged position in the universe.
The principle is named after astronomer Nicolaus Copernicus, whose work helped overturn the belief that Earth was at the center of the solar system. In modern cosmology, it supports the assumption that the universe looks broadly similar from different locations when viewed on sufficiently large scales.
The researchers’ alternative mathematical framework includes a center of spherical symmetry. This raises the question of where an observer would need to be located for the model to match 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 study opens another avenue for investigating why the universe’s expansion is accelerating. Dark energy remains a central component of widely used cosmological models, but the researchers argue that general relativity’s mathematics may 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