  The large-scale redshift-space distortion (RSD) in galaxy clustering can
probe $f\sigma_8$, a combination of the cosmic structure growth rate and the
matter fluctuation amplitude, which can constrain dark energy models and test
theories of gravity. While the RSD on small scales (e.g. a few to tens of
$h^{-1}{\rm Mpc}$) can further tighten the $f\sigma_8$ constraints, galaxy
assembly bias, if not correctly modelled, may introduce systematic
uncertainties. Using a mock galaxy catalogue with built-in assembly bias, we
perform a preliminary study on how assembly bias may affect the $f\sigma_8$
inference. We find good agreement on scales down to 8--9$h^{-1}{\rm Mpc}$
between a $f\sigma_8$ metric from the redshift-space two-point correlation
function with the central-only mock catalogue and that with the shuffled
catalogue free of assembly bias, implying that $f\sigma_8$ information can be
extracted on such scales even with assembly bias. We then apply the halo
occupation distribution (HOD) and three subhalo clustering and abundance
matching (SCAM) models to model the redshift-space clustering with the mock.
Only the SCAM model based on $V_{\rm peak}$ (used to create the mock) can
reproduce the $f\sigma_8$ metric, and the other three could not. However, the
$f\sigma_8$ metrics determined from central galaxies from all the models are
able to match the expected one down to 8$h^{-1}{\rm Mpc}$. Our results suggest
that halo models with no or incorrect assembly bias prescription could still be
used to model the RSD down to scales of $\sim 8 h^{-1}{\rm Mpc}$ to tighten the
$f\sigma_8$ constraint, with a sample of central galaxies or with a flexible
satellite occupation prescription.
