  We perform a series of cosmological hydrodynamic simulations to investigate
the effects of non-gravitational dark matter (DM) interactions on the
intergalactic medium (IGM). In particular, we use the ETHOS framework
(Cyr-Racine et al. 2016; Vogelsberger et al. 2016) to compare statistics of the
Lyman-$\alpha$ forest in cold dark matter (CDM) with an alternative model in
which the DM couples strongly with a relativistic species in the early
universe. These models are characterised by a cutoff in the linear power
spectrum, followed by a series of 'dark acoustic oscillations' (DAOs) on
sub-dwarf scales. While the primordial cutoff delays the formation of the first
galaxies, structure builds-up more rapidly in the interacting DM model compared
to CDM. We show that although DAOs are quickly washed away in the non-linear
clustering of DM at $z\lesssim10$, their signature can be imprinted prominently
in the Lyman-$\alpha$ flux power spectrum at $z>5$. On scales larger than the
cutoff ($k\sim0.08$ s/km for the specific model considered here), the relative
difference to CDM is reminiscent of a warm dark matter (WDM) model with a
similar initial cutoff; however, the redshift evolution on smaller scales is
distinctly different. The appearance and disappearance of DAOs in the
Lyman-$\alpha$ flux spectrum provides a powerful way to distinguish interacting
DM models from WDM and, indeed, variations in the thermal history of the IGM
that may also induce a small-scale cutoff.
