Stepping into the Forest: Confronting Interacting Radiation Models for the Hubble Tension with Lyman-α Data

Models of interacting dark radiation have been shown to alleviate the Hubble tension. Extensions incorporating a coupling between dark matter and dark radiation (DM-DR) have been proposed as combined solutions to both the Hubble and S₈ tensions. A key feature of these extended models is a break in the matter power spectrum (MPS), suppressing power for modes that enter the horizon before the DM-DR interactions turn off. In scenarios with a massless mediator, modes that enter before matter-radiation equality get suppressed, whereas for massive mediators, the break is determined by the mediator mass, a free parameter. In this work, we test these models against probes of LSS: weak lensing, CMB lensing, full-shape galaxy clustering, and eBOSS measurements of the 1D Lyα\, forest flux power spectrum. The latter are the most constraining since they probe small scales where many models predict the largest deviations. In fact, already within Λ CDM\,, the eBOSS Lyα\, data are in significant tension with Planck CMB data, with the Lyα\, data preferring a steeper slope of the MPS at k ~ h Mpc⁻¹. We find that the simplest dark radiation models, which improve the Hubble tension, worsen the fit to the Lyα\, data. However, models with DM-DR interactions can simultaneously address both tensions.