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

## TL;DR

This study examines the small-scale lensing discrepancy in BOSS galaxies within the Planck ΛCDM cosmology, revealing a persistent excess signal that challenges current models and suggests possible systematic effects or cosmological parameter adjustments.

## Contribution

The paper provides new measurements of galaxy lensing dependence on redshift and stellar mass, and analyzes the persistent small-scale lensing discrepancy in BOSS data.

## Key findings

- Expected small-scale lensing signal is ~25% higher than observed.
- Discrepancy persists across redshift and stellar mass ranges.
- Changing cosmological parameters alone cannot fully resolve the tension.

## Abstract

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.