In this epoch of cosmological tensions, it is essential to question the fundamental assumptions underlying our standard picture of cosmology, including the theory of gravity. The standard approach to test for deviations from General Relativity on cosmological scales is to combine measurements of the growth rate of structure with gravitational lensing. In my talk, I will demonstrate that this method suffers from an important limitation, since models of dark matter with additional interactions can lead to exactly the same signatures as modified gravity in these two observables. Luckily, I will show that the coming generation of large-scale structure surveys, like the Square Kilometer Array, will allow us to break this degeneracy through measurements of the distortion of time.
Reference paper: arXiv:2404.09379