ETHOS - an Effective Theory of Structure Formation: detecting dark matter interactions through the Lyman-$\alpha$ forest

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.