First measurement of the Weyl potential evolution from the Year 3 Dark Energy Survey data: Localising the $σ_8$ tension

Isaac Tutusaus, Camille Bonvin, Nastassia Grimm

Published 2023-12-11Version 1

We present the first measurement of the Weyl potential at four redshifts bins using data from the first three years of observations of the Dark Energy Survey (DES). The Weyl potential, which is the sum of the spatial and temporal distortions of the Universe's geometry, provides a direct way of testing the theory of gravity and the validity of the $\Lambda$CDM model. We find that the measured Weyl potential is 2.3$\sigma$, respectively 3.1$\sigma$, below the $\Lambda$CDM predictions in the two lowest redshift bins. We show that these low values of the Weyl potential are at the origin of the $\sigma_8$ tension between Cosmic Microwave Background (CMB) measurements and weak lensing measurements. Interestingly, we find that the tension remains if no information from the CMB is used. DES data on their own prefer a high value of the primordial fluctuations, followed by a slow evolution of the Weyl potential. A remarkable feature of our method is that the measurements of the Weyl potential are model-independent and can therefore be confronted with any theory of gravity, allowing efficient tests of models beyond General Relativity.