  We examine the growth of structure in three different cosmological models
with interacting dark matter and vacuum energy. We consider the case of
geodesic dark matter with zero sound speed, where the relativistic growing mode
in comoving-synchronous gauge coincides with the Newtonian growing mode at
first order in $\Lambda$CDM. We study corrections to the linearly growing mode
in the presence of interactions and the linear matter growth rate, $f_1$,
contrasting this with the velocity divergence, $f_{rsd}\sigma_8$, observed
through redshift-space distortions. We then derive second-order density
perturbations in these interacting models. We identify the reduced bispectrum
that corresponds to the non-linear growth of structure and show how the shape
of the bispectrum is altered by energy transfer to or from the vacuum. Thus the
bispectrum, or higher-order correlators, might in future be used to identify
dark matter interactions.
