New perspectives on the BOSS small-scale lensing discrepancy for the Planck $\Lambda$CDM Cosmology

We investigate the abundance, small-scale clustering and galaxy-galaxy lensing signal of galaxies in the Baryon Oscillation Spectroscopic Survey (BOSS). To this end, we present new measurements of the redshift and stellar mass dependence of the lensing properties of the galaxy sample. We analyse to what extent models assuming the Planck18 cosmology fit to the number density and clustering can accurately predict the small-scale lensing signal. In qualitative agreement with previous BOSS studies at redshift $z \sim 0.5$ and with results from the Sloan Digital Sky Survey, we find that the expected signal at small scales ($0.1 < r_{\rm p} < 3 \, h^{-1} \mathrm{Mpc}$) is higher by $\sim 25\%$ than what is measured. Here, we show that this result is persistent over the redshift range $0.1 < z < 0.7$ and for galaxies of different stellar masses. If interpreted as evidence for cosmological parameters different from the Planck CMB findings, our results imply $S_8 = \sigma_8 \sqrt{\Omega_{\rm m} / 0.3} = 0.744 \pm 0.015$, whereas $S_8 = 0.832 \pm 0.013$ for Planck18. However, in addition to being in tension with CMB results, such a change in cosmology alone does not accurately predict the lensing amplitude at larger scales. Instead, other often neglected systematics like baryonic feedback or assembly bias are likely contributing to the small-scale lensing discrepancy. We show that either effect alone, though, is unlikely to completely resolve the tension. Ultimately, a combination of the two effects in combination with a moderate change in cosmological parameters might be needed.