Researchers at the University of Genve (UNIGE) in Switzerland have developed a new method to test the famous theories of Euler and Einstein for the accelerating expansion of the universe and the nature of dark matter.

Cosmological investigations, including those using space telescopes like the Webb to peer into the ancient universe, test long-held theories about the nature of the universe, including those outlined by Leonard Euler in the 18th century and Albert Einstein in the 20th century.

“The cosmos is a unique laboratory for testing the laws of physics, especially those of Euler and Einstein. Euler described the movements of celestial objects, while Einstein described the way in which celestial objects distort the universe”, explains a statement released by UNIGE.

“Since the discovery of dark matter and the accelerating expansion of the Universe, the validity of their equations has been tested: can they explain these mysterious phenomena? A team from the University of Geneva (UNIGE) has developed the first method to find out. Consider a never-before-used measure: time warp. The results are published in *Nature astronomy*.”

Euler, whose influence is still felt today through many equations, formulas, functions and theories, provided scientists with the tools needed to calculate the motions of galaxies. Similarly, Einstein’s work underpins the modern understanding of the universe, including his famous theory of general relativity, which shows that the universe is not static and demonstrates how star clusters and galaxies distort the visible universe. .

The work of Euler and Einstein has been repeatedly tested by physicists, and so far, no discovery has significantly disrupted or completely disproved Euler or Einstein. However, the “Break All Things” phase is vital in science, and the universe is an incredibly giant laboratory, so physicists continue to evaluate the work of Euler and Einstein.

Open questions remain, especially regarding the expansion of the universe and when dark matter is considered.

“By observing galaxies located billions of light-years from Earth, researchers hope to detect signs of an effect called gravitational redshift, in which light becomes redder after escaping the gravitational pull of massive objects. This red-shifted light holds clues about how the gravitational fields of massive objects warp time, which could narrow down a number of unanswered questions about our universe,” writes Becky Ferreira for *Vice*.

“Physicists have tested these equations in all sorts of ways, which have so far proved to be effective. However, two discoveries continue to challenge these models: the accelerating expansion of the Universe and the existence of invisible dark matter, believed to account for 85% of all matter in the cosmos. Do these mysterious phenomena still obey the equations of Einstein and Euler? Researchers are not yet able to answer this question,” writes UNIGE.

“The problem is that current cosmological data do not allow us to distinguish between a theory that breaks Einstein’s equations and one that breaks Euler’s equation. This is what we demonstrate in our study. We also present a mathematical method to solve this problem. This is the culmination of ten years of research,” says Camille Bonvin, associate professor in the Department of Theoretical Physics of UNIGE’s Faculty of Science and first author of the study.

While Euler’s and Einstein’s equations can seemingly coexist in a wide range of situations, at the edge of the universe, a “missing ingredient” has been problematic. The missing ingredient is time warp measurement.

“Until then we only knew how to measure the speed of celestial objects and the sum of the distortion of time and space. We’ve developed a method to access this additional measurement, and it’s a first,” Bonvin explains.

Einstein’s theory of general relativity requires that the time warp equals the sum of time and space. If not, then Einstein’s model, which has so far passed every test, no longer applies to the entire universe.

Poking and prodding Einstein’s theory to see if it holds up is nothing new. Einstein’s work has come under scrutiny since the general theory of relativity passed its first significant test in 1919. Physicists have also worked to create rival explanations for the workings of the universe in case the theory is found to of Einstein fails.

Current understanding of dark matter and dark energy is based on assumptions derived from the general theory of relativity, so if new research and measurements challenge Einstein’s theory, then cosmological hell breaks loose.

“This will allow us to find out whether there are new forces or matter in the Universe that violate these two theories,” explains Levon Pogosian, co-author of the study and professor in the Physics Department of Simon Fraser University in Canada.

The measurement method proposed by Bonvin and Pogosian will be tested shortly. The study’s findings contribute to several ongoing missions, including the launch of the European Space Agency’s EUCLID space telescope next month and the Dark Energy Spectroscopic Instrument (DESI) project which is currently making observations. The method will also be integrated into the giant Square Kilometer Array (SKA) radio telescope which will begin observing deep space from South Africa and Australia in 2028 or 2029.

“Our method will be integrated into these different missions. This is already the case with DESI, of which we have become external collaborators thanks to this research,” says Bonvin.

“The research team successfully tested its model on synthetic catalogs of galaxies. The next phase will consist in testing it using the first data provided by DESI, as well as in identifying obstacles and minimizing systematic features that could hinder its application,” explains UNIGE.

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