  Atomic dark matter is a simple but highly theoretically motivated possibility
for an interacting dark sector that could constitute some or all of dark
matter. We perform a comprehensive study of precision cosmological observables
on minimal atomic dark matter, exploring for the first time the full parameter
space of dark QED coupling and dark electron and proton masses $(\alpha_{D},
m_{e_{D}}, m_{p_{D}})$ as well as the two cosmological parameters of aDM mass
fraction $f_{D}$ and temperature ratio $\xi$ at time of SM recombination. We
also show how aDM can accommodate the $(H_0, S_8)$ tension from late-time
measurements, leading to a better fit than $\Lambda$CDM or $\Lambda$CDM + dark
radiation. Furthermore, including late-time measurements leads to closed
contours of preferred $\xi$ and dark hydrogen binding energy. The dark proton
mass is seemingly unconstrained. Our results serve as an important new
jumping-off point for future precision studies of atomic dark matter at
non-linear and smaller scales.

High Energy Physics - Phenomenology;Cosmology and Nongalactic Astrophysics