Hubble and Friedman observed in the 30' that our universe is in expansion. According to Einstein's theory of gravity, General Relativity, it was expected that this expansion should slow down as time evolves. Surprisingly, in 1998 two groups of astrophysicists observed the opposite: that the expansion of our universe is accelerating. Since then cosmologists have tried to understand what is causing this acceleration. Two types of mechanisms have been proposed: the first one consists in adding a new form of energy in our universe, called dark energy, that would be responsible for the accelerated expansion. The second possibility is to modify the laws of gravity at large distances, such that gravity itself would make the universe expand faster and faster. In this context, the aim of my project is to test the laws of gravity at very large distances, to understand if General Relativity is still valid at the scale of the universe or if it has to be replaced by another theory of gravity. Since gravity is one of the fundamental laws of physics, it is of great importance to determine what its true nature is.
To achieve this goal, with my team we have designed new methods to test some fundamental properties of gravity at large distances. First we have identified a key quantity, gravitational redshift, which impacts our observations of galaxies. We have constructed a method to measure this quantity and we have demonstrated that it will be detectable with the coming observations from the DESI and Euclid surveys. We are now applying the method to the first data delivered by DESI. Second, we have demonstrated that gravitational redshift, which is sensitive to the distortion of time, is a key quantity to robustly test gravity. Without this observable, deviations from General Relativity would be degenerated with additional forces acting on dark matter, preventing us to test gravity robustly. The distortion of time provides the missing ingredient to test gravity and dark matter without ambiguity and to clearly discriminate between their signatures. Finally, in the course of the project we have developed a method to extract the Weyl potential, which is the sum of the spatial and temporal distortions of the geometry, from gravitational lensing. We have measured this observable in the Dark Energy Survey and used it to test gravity and dark matter. Together, the distortion of time, the velocity of galaxies and the Weyl potential allow us to look for deviations from our standard model of cosmology in an optimal and robust way.
