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We introduce a novel technique for constraining cosmological parameters andgalaxy assembly bias using non-linear redshift-space clustering of galaxies. Wescale cosmological N-body simulations and insert galaxies with the SubHaloAbundance Matching extended (SHAMe) empirical model to generate over 175,000clustering measurements spanning all relevant cosmological and SHAMe parametervalues. We then build an emulator capable of reproducing the projected galaxycorrelation function at the monopole, quadrupole and hexadecapole level forseparations between $0.1\,h^{-1}{\rm Mpc}$ and $25\,h^{-1}{\rm Mpc}$. We testthis approach by using the emulator and Monte Carlo Markov Chain (MCMC)inference to jointly estimate cosmology and assembly bias parameters both forthe MTNG740 hydrodynamic simulation and for a semi-analytical galaxy formationmodel (SAM) built on the MTNG740-DM dark matter-only simulation, obtainingunbiased results for all cosmological parameters. For instance, for MTNG740 anda galaxy number density of $n\sim 0.01 h^{3}{\rm Mpc}^{-3}$, we obtain$\sigma_{8}=0.799^{+0.039}_{-0.044}$ ($\sigma_{8,{\rm MTNG}} =$ 0.8159), and$\Omega_\mathrm{M}h^2= 0.138^{+ 0.025}_{- 0.018}$ ($\Omega_{\mathrm{M}}h^2_{\rm MTNG} =$ 0.142). For fixed Hubble parameter ($h$), the constraintbecomes $\Omega_\mathrm{M}h^2= 0.137^{+ 0.011}_{- 0.012}$. Our method performssimilarly well for the SAM and for other tested sample densities. We almostalways recover the true amount of galaxy assembly bias within one sigma. Thebest constraints are obtained when scales smaller than $2\,h^{-1}{\rm Mpc}$ areincluded, as well as when at least the projected correlation function and themonopole are incorporated. These methods offer a powerful way to constraincosmological parameters using galaxy surveys.

The MillenniumTNG Project: Inferring cosmology from galaxy clustering with accelerated N-body scaling and subhalo abundance matching