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The halo model with beyond-linear halo bias: unbiasing cosmological constraints from galaxy-galaxy lensing and clustering

We determine the error introduced in a joint halo model analysis of galaxy-galaxy lensing and galaxy clustering observables when adopting the standard approximation of linear halo bias. Considering the Kilo-Degree Survey, we forecast that ignoring the non-linear halo bias would result in up to 5$σ$ offsets in the recovered cosmological parameters describing structure growth, $S_8$, and the matter density parameter, $Ω_{\mathrm{m}}$. We include the scales $10^{-1.3}<r_{\rm{p}} \ / h^{-1}\, \mathrm{Mpc}<10$ in the data vector, and the direction of these offsets are shown to depend on the freedom afforded to the halo model through other nuisance parameters. We conclude that a beyond-linear halo bias correction must therefore be included in future cosmological halo model analyses of large-scale structure observables on non-linear scales.