Probing solutions to the $S_8$ tension with galaxy clustering

The current discrepancy between the CMB and weak lensing measurements of the amplitude of matter fluctuations, the so-called $S_8$ tension, has attracted a great deal of recent attention, as it may show a crack in the $\Lambda$CDM model of cosmology. We review the evidence for this tension and describe potential solutions, focusing on extensions of the standard cosmological model, including interacting dark energy and modified gravity. We present a likelihood analysis of the BOSS DR12 data, probing these alternative models as well as $\Lambda$CDM. From this analysis, we show hints of non-standard cosmology compatible with those seen in weak lensing observations, demonstrating that interacting dark energy or modified gravity can explain them successfully. We then discuss the robustness of these results to analysis choices, as well as future paths to confirm them with additional data and further distinguish between models.