Late time modification of structure growth and the S8 tension

The S₈ tension between low-redshift galaxy surveys and the primary cosmic microwave background (CMB) signals a possible breakdown of the ΛCDM model. Recently differing results have been obtained using low-redshift galaxy surveys and the higher redshifts probed by CMB lensing, motivating a possible time-dependent modification to the growth of structure. We investigate a simple phenomenological model in which the growth of structure deviates from the ΛCDM prediction at late times, in particular as a simple function of the dark energy density. Fitting to galaxy lensing, CMB lensing, baryon acoustic oscillations, and supernovae datasets, we find significant evidence---2.5--3σ, depending on analysis choices---for a nonzero value of the parameter quantifying a deviation from ΛCDM. The preferred model, which has a slower growth of structure below z~1, improves the joint fit to the data over ΛCDM. While the overall fit is improved, there is weak evidence for galaxy and CMB lensing favoring different changes in the growth of structure.