Testing Universe’s Mysteries: Are Einstein and Euler’s Equations Up to the Task?

University of Geneva researchers have developed the first-ever method to test if mysterious phenomena like dark matter and accelerated universal expansion can be explained by Euler’s and Einstein’s equations. The method involves measuring time distortion – an aspect not previously used. The technique will be integrated into major space missions and observatories.

Scientists from the University of Geneva (UNIGE) have created a breakthrough method to ascertain if the equations by Euler and Einstein can account for the mysteries of dark matter and the accelerating expansion of the Universe. The method, which is unprecedented, measures time distortion. This development has been published in Nature Astronomy.

Leonhard Euler and Albert Einstein formulated equations that have been foundational in understanding the Universe. Euler’s equation aids in calculating the motion of galaxies, while Einstein’s theory of general relativity shows that star clusters and galaxies can distort the Universe.

Einstein’s and Euler’s equations have withstood various tests but have been challenged by the discovery of dark matter and the accelerating expansion of the Universe. Up until now, scientists have been unable to determine whether these equations can explain these phenomena.

Camille Bonvin, an associate professor at UNIGE and the study’s first author, said, “The problem is that current cosmological data do not allow us to differentiate 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 for solving this problem. This is the culmination of ten years of research”.

This method hinges on measuring time distortion, an element not factored in before. Camille Bonvin explained, “Until then, we only knew how to measure the speed of celestial objects and the sum of the distortion of time and space. We have developed a method for accessing this additional measurement, and it’s a first”.

If there are discrepancies in time distortion relative to the sum of time and space, it indicates that Einstein’s model might be flawed. If time distortion does not align with the speed of galaxies as per Euler’s equation, Euler’s equation could be invalidated. Levon Pogosian, a professor at Simon Fraser University and co-author of the study, said, “This will allow us to discover whether new forces or matter, which violate these two theories, exist in the Universe”.

This method is pivotal and will be integrated into several space missions including the EUCLID space telescope launching in July 2023, the Dark Energy Spectroscopic Instrument (DESI), and the international SKA giant radio telescope project.

Camille Bonvin added, “Our method will be integrated into these different missions. This is already the case for DESI, whom we have become external collaborators thanks to this research”. The team has successfully tested the method using synthetic galaxy catalogues. The next steps involve testing with real data from DESI and refining the method to overcome potential challenges.


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