# Cosmology with galaxy-galaxy lensing on non-perturbative scales: Emulation method and application to BOSS LOWZ

## TL;DR

This paper introduces a nonlinear emulation framework combining HOD models and N-body simulations to accurately predict galaxy clustering and lensing signals, applied to BOSS LOWZ data to measure cosmological parameters.

## Contribution

The paper presents a novel emulation method that achieves high accuracy in modeling galaxy signals on non-perturbative scales, enabling improved cosmological parameter estimation.

## Key findings

- Achieved <2% interpolation accuracy across parameter space.
- Recovered true S_8 value from mock data.
- Measured S_8=0.847±0.037 from BOSS LOWZ data, in tension with Planck results.

## Abstract

We describe our nonlinear emulation (i.e., interpolation) framework that combines the halo occupation distribution (HOD) galaxy bias model with $N$-body simulations of nonlinear structure formation, designed to accurately predict the projected clustering and galaxy-galaxy lensing signals from luminous red galaxies (LRGs) in the redshift range $0.16 < z < 0.36$ on comoving scales $0.6 < r_p < 30$ \hMpc. The interpolation accuracy is $\lesssim 1-2$ per cent across the entire physically plausible range of parameters for all scales considered. We correctly recover the true value of the cosmological parameter $S_8 = ({\sigma_8}/{0.8228}) ({\Omega_{\text{m}}}/{0.3107})^{0.6}$ from mock measurements produced via subhalo abundance matching (SHAM)-based lightcones designed to approximately match the properties of the SDSS LOWZ galaxy sample. Applying our model to Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 14 (DR14) LOWZ galaxy clustering and galaxy-shear cross-correlation measurements made with Sloan Digital Sky Survey (SDSS) Data Release 8 (DR8) imaging, we perform a prototype cosmological analysis marginalizing over $w$CDM cosmological parameters and galaxy HOD parameters. We obtain a 4.4 per cent measurement of $S_8 = 0.847 \pm 0.037$, in $3.5\sigma$ tension with the Planck cosmological results of $1.00 \pm 0.02$. We discuss the possibility of underestimated systematic uncertainties or astrophysical effects that could explain this discrepancy.