Einstein’s equations, if applied more carefully, may hold the answer to why the universe is expanding faster, without any need for mysterious dark energy, say scientists

For almost three decades, dark energy has been the standard explanation for why the universe is expanding at an accelerating rate. Now, a team of mathematicians is challenging this widely accepted theory. The mathematicians at the University of California, Davis, argue that the answer may already lie within Einstein’s own equations and that an invisible form of energy may not be needed at all. The findings are published in the journal Proceedings of the Royal Society A. The researchers worked with the Einstein-Euler equations, which combine Einstein’s general relativity with the rules that govern how fluids move. They used these tools to test the leading framework for explaining the universe’s evolution since the Big Bang, known as the Lambda-cold dark matter model, and found a weak spot in its very foundation.

Einstein’s equations may explain

Blake Temple, the study’s corresponding author and a professor emeritus of mathematics at UC Davis, offered a simple comparison: a pencil balanced vertically on its tip. “All the forces are in balance when a pencil is standing on end, so it is a ‘solution’ of the equations. But it’s unstable. Any breath of air and it falls away,” Temple said in a release.According to him, the standard model behaves in a similar way. The mathematical structures at its core, known as Friedmann spacetimes, are unstable, and the standard solution is unusually fragile. Physicists tend to treat unstable solutions as unphysical. “Unstable solutions in physics and science are considered not physical. You’ll never observe them in nature,” Temple said. If the real universe drifts away from that model, the team argues, the accelerating expansion may not require a separate source of energy. The researchers say the answer is already contained in 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.

Early expansion linked to a shockwave?

The research did not begin as a rethink of cosmology. According to Temple, the team first wondered whether a massive shockwave could explain the early expansion, with the unexpected acceleration coming from a wave trailing behind it. This very question led them to these findings. “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. Then we realised there’s a family of self-similar solutions during the radiation epoch of the Big Bang, which might model that expanding wave,” Temple said.The researchers used Einstein’s equations to examine whether the standard model of the universe remains stable when slightly disturbed. They found that these disturbances grow rather than fade away during the period when matter dominated the universe. The results are striking. They suggest that the conventional mathematical descriptions of the expanding universe are vulnerable to disturbances that grow rather than fade.“We prove that, like Einstein’s static model, the Friedmann spacetimes are all unstable to radial perturbation at large length scales. 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,” Temple said.The researchers found that radial disturbances could cause the universe to expand differently from what the standard model predicts. “This means that the Big Bang should generically look exactly like a Friedmann spacetime near the centre of symmetry, but generically one should observe accelerations away from Friedmann far from the centre,” he explained.The researchers also raise an older idea: the Copernican principle. Named after Nicolaus Copernicus, it holds that Earth and its observers do not occupy a special position in the universe. The Copernican principle must be applied consistently when evaluating competing explanations of the universe, Temple argues.“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. If this principle rules out one, it has to rule out the other,” Temple said.The research was supported by the United Kingdom’s Engineering and Physical Sciences Research Council and the American Institute of Mathematics SQuaREs Program.