Constraining long-lived dark sector particles with CMB and Lyman-$\alpha$

We use measurements of the intergalactic medium (IGM) temperature from the Lyman-$\alpha$ forest to place new limits on models in which long-lived dark sector (DS) particles, with lifetimes longer than $10^{16}$ s, deposit energy into the IGM through their decays. Such DS decays into Standard Model (SM) states can modify the late-time thermal history of the IGM, making Lyman-$\alpha$ data a sensitive probe of hidden sectors with cosmologically long lifetimes. Our analysis demonstrates that constraints from late-time IGM heating offer a complementary window to those from the Cosmic Microwave Background (CMB), in constraining dark sector parameter space. We further revisit limits on such decaying DS models from Planck's measurements of the optical depth to reionization and provide updates relevant for DS lifetimes longer than $10^{14}$ s. The model-independent constraints on the DS parameter space we derive in this work can be reinterpreted for a wide range of decaying hidden-sector scenarios, including evaporating primordial black holes and SM-coupled dark photons.