Mathematicians at the University of California, Davis, have presented a significant challenge to the prevailing explanation for the accelerating expansion of the universe. In a study published in Proceedings of the Royal Society A, the team argues that the standard model relies on a mathematical framework that is inherently unstable. Their calculations suggest that cosmic acceleration could emerge naturally from Einstein's original theory of gravity, potentially eliminating the need for the mysterious component known as dark energy.
The research focuses on the Lambda-cold dark matter model, which has been the leading framework for describing the universe's evolution since the Big Bang. By analyzing the Einstein-Euler equations, which combine general relativity with fluid dynamics, the researchers found that Friedmann spacetimes—the foundation of conventional expansion models—are unstable at both small and large scales. Blake Temple, the study's corresponding author and a distinguished professor emeritus of mathematics at UC Davis, compared this instability to a pencil balanced vertically on its tip. While such a state represents a solution where forces are in balance, it is physically unobservable because any minor disturbance causes it to collapse.
Temple explained that unstable solutions in physics are generally considered non-physical because they would never be observed in nature. The team's analysis indicates that the universe naturally evolves away from the behavior predicted by these conventional models. Consequently, the accelerating expansion might not require a separate form of energy to explain it. Instead, the answer could already be contained within Einstein's original equations, offering a simpler and more natural explanation than dark energy.
For nearly three decades, dark energy has been the primary explanation for the discovery that the universe is not just expanding, but accelerating. This concept traces back to Einstein's 1915 theory of general relativity. Although Einstein initially introduced a "cosmological constant" to maintain a static universe—a move he later called his biggest blunder after Edwin Hubble discovered expansion in 1929—the term returned to prominence in the 1990s when astronomers observed speeding up cosmic expansion. Today, this is associated with dark energy within the standard Friedmann universe model, which assumes space expands while matter remains evenly distributed.
The researchers initially explored whether a massive shockwave could explain the expansion and its acceleration. They identified a family of self-similar solutions during the radiation epoch of the Big Bang that might model an expanding wave. Using a self-similar form of Einstein's equations, they treated the standard cosmological model as a rest point to examine how small departures from this state would behave over time. Their results suggest that conventional descriptions are vulnerable to disturbances that grow rather than fade.
Temple stated that their work proves Friedmann spacetimes are unstable to radial perturbation at large length scales, similar to Einstein's static model. This instability appears to rule out the Lambda-cold dark matter model as a viable stable solution of the Einstein equations, regardless of whether dark energy is included. Radial perturbations, which change with distance from a central point, can cause an expanding universe to depart from standard predictions. The researchers argue that while the Big Bang might look like a Friedmann spacetime near a center of symmetry, observers far from this center would generically observe accelerations.
Beyond the implications for dark energy, the study raises fundamental questions regarding the Copernican principle, which holds that our location in the universe is not special or privileged. The researchers' alternative framework introduces a center of spherical symmetry, prompting inquiries about where an observer must be located for the model to align with observations. Temple argued that both the standard Lambda-cold dark matter model and a spherically symmetric spacetime produce a special place where observers must lie for the models to be physically plausible. He noted that if the Copernican principle rules out one, it must rule out the other.
The findings represent a theoretical challenge to standard cosmology rather than observational proof that dark energy is unnecessary. Determining whether this alternative can describe the actual universe will require assessing how well its predictions match astronomical observations. If further theoretical and observational work supports their interpretation, it could lead to a significant reassessment of how scientists understand cosmic expansion and the mathematical foundations of the Big Bang. The research received funding from the United Kingdom's Engineering and Physical Sciences Research Council and the American Institute of Mathematics SQuaREs Program.
Sources: ScienceDaily.