  Combining galaxy clustering information from regions of different
environmental densities can help break cosmological parameter degeneracies and
access non-Gaussian information from the density field that is not readily
captured by the standard two-point correlation function (2PCF) analyses.
However, modelling these density-dependent statistics down to the non-linear
regime has so far remained challenging. We present a simulation-based model
that is able to capture the cosmological dependence of the full shape of the
density-split clustering (DSC) statistics down to intra-halo scales. Our models
are based on neural-network emulators that are trained on high-fidelity mock
galaxy catalogues within an extended-$\Lambda$CDM framework, incorporating the
effects of redshift-space, Alcock-Paczynski distortions and models of the
halo-galaxy connection. Our models reach sub-percent level accuracy down to
$1\,h^{-1}{\rm Mpc}$ and are robust against different choices of galaxy-halo
connection modelling. When combined with the galaxy 2PCF, DSC can tighten the
constraints on $\omega_{\rm cdm}$, $\sigma_8$, and $n_s$ by factors of 2.9,
1.9, and 2.1, respectively, compared to a 2PCF-only analysis. DSC additionally
puts strong constraints on environment-based assembly bias parameters. Our code
is made publicly available on Github.
