AV¶ÌÊÓƵ

A Precision Test of General Relativity

While Einstein’s famous theory of general relativity accurately describes the motion of celestial bodies in our solar system, less is known about the laws of gravity at the scales of our cosmos. One possibility to explain the observed accelerated expansion in our Universe consists of deviations from Einstein’s theory - so called modifications of gravity - across large distances. Now, in a study published in Physical Review Letters, a team of researchers from Université de Genève and Université de Toulouse has designed a novel method for a precision test of general relativity by combining galaxy velocities and spacetime distortions.

On Earth, the laws of gravity can be tested accurately in laboratory experiments. Similarly, our Solar System provides ideal settings to test the theory of general relativity: by precisely tracing the orbits of celestial bodies, such as the planet Mercury, Einstein’s predictions have been proven with great precision. However, beyond the scales of individual solar systems and galaxies, assessing the laws of gravity becomes more difficult and requires special methods. One possibility is to exploit the effect of weak gravitational lensing: as light from distant galaxies travels across the Universe to reach our telescopes, it is influenced by the presence of matter along its path. “More precisely, in the language of general relativity, the paths of light particles are affected by the presence of spacetime distortions caused by matter“, explains Nastassia Grimm, postdoctoral researcher at the AV¶ÌÊÓƵ, and first author of the study. The resulting deflection of light generates tiny distortions in the observed shapes of galaxies that can be inferred statistically when combining millions of galaxies. “Measuring these distorted shapes tells us about the depth of spacetime distortions, and thus about the fundamental laws of gravity that link them to matter“, resumes Grimm. In a previous work published in Nature Communications, the researchers from Toulouse and Geneva have exploited this fact to measure the Weyl potential evolution, providing a robust measure of spacetime distortions at different epochs of the history of the Universe.

A second way scientists can probe gravity is by studying galaxy velocities. “Galaxy velocities are influenced by gravity, caused by other galaxies present in the Universe“, explains Camille Bonvin, associate professor at the AV¶ÌÊÓƵ and co-author of the study. “This causes a subtle coherent motion of galaxies, which depends on the specific laws of gravity governing the Universe“ she adds. While the velocities of distant galaxies cannot be measured directly, scientists can use a phenomenon known as redshift-space distortions: large structures formed by galaxies appear to be squeezed along the line of sight, an effect caused by the influence of galaxy velocities on how their positions are observed.

Redshift-distortions and gravitational lensing can be combined for a test of gravity called the E_G statistic, which consists of comparing the way galaxies move with how the geometry of space and time is distorted. While in general relativity, this relation is given by its theoretical prediction, a modification of gravity would break that link. In their recent work, the scientists from Geneva and Toulouse have developed and applied a new method to measure the E_G statistic, by using redshift-space distortions together with the Weyl potential evolution. “With our new method, we have achieved a considerable improvement in precision compared to previous measurements of the E_G statistic. This advancement can help us to gain new knowledge of how gravity behaves across vast distances“, says Bonvin.

While the authors’ new measurements of the E_G statistic do not reveal any significant deviation from Einstein’s theory, they advise caution before drawing definite conclusions about the absence or presence of modifications of gravity. “The measurement of the Weyl potential on its own shows a mild tension with predictions in general relativity. Taking the ratio of the potential with velocities to build E_G increases the uncertainty, consequently decreasing the tension“, comments Isaac Tutusaus, associate professor at Université de Toulouse and co-author of the study. “The new generation of surveys, such as the Euclid mission, the Vera C. Rubin Observatory or the Dark Energy Spectroscopic Instrument, is expected to deliver cosmological data of unprecedented wealth and precision in the coming years, allowing us to drastically improve the measurement of E_G“, he concludes.

With their work, the researchers from Geneva and Toulouse have set a crucial milestone towards robust tests of gravity, paving the way for a deeper understanding of the fundamental laws of physics that govern our cosmos.