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There is untapped cosmological information in galaxy redshift surveys in thenon-linear regime. In this work, we use the AEMULUS suite of cosmological$N$-body simulations to construct Gaussian process emulators of galaxyclustering statistics at small scales ($0.1-50 \: h^{-1}\,\mathrm{Mpc}$) inorder to constrain cosmological and galaxy bias parameters. In addition tostandard statistics -- the projected correlation function$w_\mathrm{p}(r_\mathrm{p})$, the redshift-space monopole of the correlationfunction $\xi_0(s)$, and the quadrupole $\xi_2(s)$ -- we emulate statisticsthat include information about the local environment, namely the underdensityprobability function $P_\mathrm{U}(s)$ and the density-marked correlationfunction $M(s)$. This extends the model of AEMULUS III for redshift-spacedistortions by including new statistics sensitive to galaxy assembly bias. Inrecovery tests, we find that the beyond-standard statistics significantlyincrease the constraining power on cosmological parameters of interest:including $P_\mathrm{U}(s)$ and $M(s)$ improves the precision of ourconstraints on $\sigma_8$ by 33%, $\Omega_m$ by 28%, and the growth ofstructure parameter, $f \sigma_8$, by 18% compared to standard statistics. Weadditionally find that scales below $4 \: h^{-1}\,\mathrm{Mpc}$ contain as muchinformation as larger scales. The density-sensitive statistics also contributeto constraining halo occupation distribution parameters and a flexibleenvironment-dependent assembly bias model, which is important for extractingthe small-scale cosmological information as well as understanding thegalaxy-halo connection. This analysis demonstrates the potential of emulatingbeyond-standard clustering statistics at small scales to constrain the growthof structure as a test of cosmic acceleration. Our emulator is publiclyavailable at https://github.com/kstoreyf/aemulator.

The Aemulus Project VI: Emulation of beyond-standard galaxy clustering statistics to improve cosmological constraints