Joint analysis of small-scale galaxy clustering and galaxy--galaxy lensing from BOSS galaxies

We present a joint analysis of galaxy clustering and galaxy--galaxy lensing measurements from BOSS galaxies using a simulation-based emulation method combined with a halo occupation distribution model. Our emulators are constructed with the Aemulus $\nu$ simulations, a suite of $w\nu$CDM $N$-body simulations with massive neutrinos as independent particle species. We combine small-scale analysis of clustering from $0.1h^{-1}$Mpc to $60.2~h^{-1}$Mpc and lensing from $1.7h^{-1}$Mpc to $60.2~h^{-1}$Mpc to perform cosmological constraints. We split the BOSS galaxies into three redshift bins to measure their clustering and employ galaxies from Dark Energy Camera Legacy Survey and Hyper Suprime-Cam as source galaxies to measure lensing separately. We find that the addition of lensing significantly improves the constraining power on $S_{8}=\sigma_8(\Omega_m/0.3)^{0.5}$, with a weak improvement for $f\sigma_{8}$. Our results of $f\sigma_{8}$ indicate tensions of around $1\sim4\sigma$ below the results of CMB observations of Planck. For $S_{8}$, our results are also lower than Planck, and the tension can be mitigated when considering possible systematics in lensing measurement. As a byproduct, our analysis prefers a non-zero neutrino mass but without strong significance, with the constraining power dominated by the clustering. Given the accuracy and precision of our model and the observational data, it is anticipated that larger and higher-quality spectroscopic datasets will improve the constraints on this fundamental property in the near future.