Modelling galaxy clustering in redshift space with a Lagrangian bias formalism and $N$-body simulations

Improving the theoretical description of galaxy clustering on small scales is an important challenge in cosmology, as it can considerably increase the scientific return of forthcoming galaxy surveys -- e.g. tightening the bounds on neutrino masses and deviations from general relativity. In this paper, we propose and test a new model for the clustering of galaxies that is able to accurately describe redshift-space distortions even down to small scales. This model corresponds to a second-order perturbative Lagrangian bias expansion which is advected to Eulerian space employing a displacement field extracted from $N$-body simulations. Eulerian coordinates are then transformed into redshift space by directly employing simulated velocity fields augmented with nuisance parameters capturing various possible satellite fractions and intra-halo small-scale velocities. We quantify the accuracy of our approach against samples of physically-motivated mock galaxies selected according to either Stellar Mass (SM) or Star Formation Rate (SFR) at multiple abundances and at $z=0$ and $1$. We find our model describes the monopole, quadrupole, and hexadecapole of the galaxy-power spectra down to scales of $k\approx 0.6 [h/$Mpc] within the accuracy of our simulations. This approach could pave the way to significantly increase the amount of cosmological information to be extracted from future galaxy surveys.