Ever since the Planck satellite measured the cosmic microwave background (CMB) down to arcminute angular scales, the mismatch between the CMB-inferred value of the Hubble constant and the value inferred from the distance ladder (i.e., the Hubble tension) has been a growing concern and is currently at the $\sim 6\sigma$ level. There are a handful of proposed mechanisms operating in the early Universe which have shown some promise in resolving the Hubble tension. These mechanisms are expected to leave a measurable impact on the smallest-scale CMB anisotropy, deep in the damping tail. Using current CMB data, baryonic acoustic oscillation data, and the luminosities of type Ia supernovae as a baseline, we compute the predicted small-scale CMB power spectra for a characteristic set of these models. We find that near-future CMB data should be able to distinguish some but not all of the investigated models from the core cosmological model, $\mathrm{\Lambda }\mathrm{CDM}$.

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• Baryon acoustic oscillations
• Cosmic microwave background
• Cosmological parameters
• Particle astrophysics