Late Time Modification of Structure Growth and the S8 Tension

The $S_8$ tension between low-redshift galaxy surveys and the primary CMB signals a possible breakdown of the $\Lambda$CDM 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 $\Lambda$CDM prediction at late times, in particular as a simple function of the dark energy density. Fitting to galaxy lensing, CMB lensing, BAO, and Supernovae datasets, we find significant evidence - 2.5 - 3$\sigma$, depending on analysis choices - for a non-zero value of the parameter quantifying a deviation from $\Lambda$CDM. The preferred model, which has a slower growth of structure below $z\sim 1$, improves the joint fit to the data over $\Lambda$CDM. While the overall fit is improved, there is weak evidence for galaxy and CMB lensing favoring different changes in the growth of structure.
Comment: Match the published version. Add more references. 6 pages, 5 figures, 1 table