Constraints on Dark Matter-Baryon Scattering from the Temperature Evolution of the Intergalactic Medium

The thermal evolution of the intergalactic medium (IGM) can serve as a sensitive probe of cosmological heat sources and sinks. We employ it to limit interactions between dark matter and baryons. After reionization the IGM temperature is set by the balance between photoheating and adiabatic cooling. We use measurements of the IGM temperature from Lyman-$\alpha$-forest data to constrain the cross-section $\sigma$ between dark matter and baryons, finding $\sigma <{10}^{-20}$ cm${}^2$ for dark-matter masses $m_{\chi }\le 1$ GeV. This provides the first direct constraint on scattering between dark matter and baryons at redshift $z\sim 5$.