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A<sc>bstract</sc> 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 (α_D,$$ {m}_{e_D} $$ $m_{e_D}$,$$ {m}_{p_D} $$ $m_{p_D}$) as well as the two cosmological parameters of aDM mass fractionf_Dand temperature ratioξat time of SM recombination. We also show how aDM can accommodate the (H₀, S₈) tension from late-time measurements, leading to a better fit than ΛCDM or ΛCDM + dark radiation. Furthermore, including late-time measurements leads to closed contours of preferredξand 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. 

A bstract The mirror twin Higgs model (MTH) is a solution to the Higgs hierarchy problem that provides well-predicted cosmological signatures with only three extra parameters: the temperature of the twin sector, the abundance of twin baryons, and the vacuum expectation value (VEV) of twin electroweak symmetry breaking. These parameters specify the behavior of twin radiation and the acoustic oscillations of twin baryons, which lead to testable effects on the cosmic microwave background (CMB) and large-scale structure (LSS). While collider searches can only probe the twin VEV, through a fit to cosmological data we show that the existing CMB (Planck18 TTTEEE+lowE+lowT+lensing) and LSS (KV450) data already provide useful constraints on the remaining MTH parameters. Additionally, we show that the presence of twin radiation in this model can raise the Hubble constant H 0 while the scattering twin baryons can reduce the matter fluctuations S 8 , which helps to relax the observed H 0 and S 8 tensions simultaneously. This scenario is different from the typical ΛCDM + ∆ N eff model, in which extra radiation helps with the Hubble tension but worsens the S 8 tension. For instance, when including the SH0ES and 2013 Planck SZ data in the fit, we find that a universe with ≳ 20% of the dark matter comprised of twin baryons is preferred over ΛCDM by ∼ 4 σ . If the twin sector is indeed responsible for resolving the H 0 and S 8 tensions, future measurements from the Euclid satellite and CMB Stage 4 experiment will further measure the twin parameters to O (1 − 10%)-level precision. Our study demonstrates how models with hidden naturalness can potentially be probed using precision cosmological data.