Validating a minimal galaxy bias method for cosmological parameter inference using HSC-SDSS mock catalogs

We assess the performance of a perturbation theory inspired method for inferring cosmological parameters from the joint measurements of galaxy-galaxy weak lensing ($\Delta\Sigma$) and the projected galaxy clustering ($w_{\rm p}$). To do this, we use a wide variety of mock galaxy catalogs constructed based on a large set of $N$-body simulations that mimic the Subaru HSC-Y1 and SDSS galaxies, and apply the method to the mock signals to address whether to recover the underlying true cosmological parameters in the mocks. We find that, as long as the appropriate scale cuts, $12$ and $8~h^{-1}{\rm Mpc}$ for $\Delta\Sigma$ and $w_{\rm p}$ respectively, are adopted, a "minimal-bias" model using the linear bias parameter $b_1$ alone and the nonlinear matter power spectrum can recover the true cosmological parameters (here focused on $\Omega_{\rm m}$ and $\sigma_8$) to within the 68% credible interval, for all the mocks we study including one in which an assembly bias effect is implemented. This is as expected if physical processes inherent in galaxy formation/evolution are confined to local, small scales below the scale cut, and thus implies that real-space observables have an advantage in filtering out the impact of small-scale nonlinear effects in parameter estimation, compared to their Fourier-space counterparts. In addition, we find that a theoretical template including the higher-order bias contributions such as nonlinear bias parameter $(b_2)$ does not improve the cosmological constraints, but rather leads to a larger parameter bias compared to the baseline $b_1$-method.