Searching for blue in the dark

The primordial power spectrum of curvature perturbations has been well-measured on large scales but remains fairly unconstrained at smaller scales, where significant deviations from $\Lambda$CDM may occur. Measurements of 21-cm intensity mapping in the dark ages promise to access very small scales that have yet to be probed, extending beyond the reach of cosmic microwave background and galaxy surveys. In this paper, we investigate how small-scale power-law enhancements -- or blue tilts -- of the primordial power spectrum affect the 21-cm power spectrum. We consider generic enhancements due to curvature modes, isocurvature modes, and runnings of the spectral tilt. We present forecasts for Earth- and lunar-based instruments to detect a blue-tilted primordial spectrum. We find that an Earth-based instrument capable of reaching the dark ages could detect any enhancements of power on nearly all the scales it can observe, which depends on the baseline of the interferometer. The smallest scales observed by such an instrument can only detect a very strong enhancement. However, an instrument on the far side of the Moon of the same size would be able to probe shallower slopes with higher precision. We forecast results for instruments with $100 \, {\rm km} \, (3000 \, {\rm km})$ baselines and find that they can probe up to scales of order $k_{\rm max} \sim 8 \, {\rm Mpc}^{-1} \, (k_{\rm max} \sim 250 \, {\rm Mpc}^{-1})$, thereby providing invaluable information on exotic physics and testing inflationary models on scales not otherwise accessible.