The observation of space-time variations in fundamental constants would provide strong evidence for the existence of new light degrees of freedom in the theory of Nature. Robustly constraining such scenarios requires exploiting observations that span different scales and probe the state of the Universe at different epochs. In the context of cosmology, both the cosmic microwave background and the Lyman-$alpha$ forest have proven to be powerful tools capable of constraining variations in electromagnetism, however at the moment there do not exist cosmological probes capable of bridging the gap between recombination and reionization. In the near future, radio telescopes will attempt to measure the 21cm transition of neutral hydrogen during the epochs of reionization and the cosmic dawn (and potentially the tail end of the dark ages); being inherently sensitive to electromagnetic phenomena, these experiments will offer a unique perspective on space-time variations of the fine-structure constant and the electron mass. We show here that large variations in these fundamental constants would produce features on the 21cm power spectrum that may be distinguishable from astrophysical uncertainties. Furthermore, we forecast the sensitivity for the Square Kilometer Array, and show that the 21cm power spectrum may be able to constrain variations at the level of ${cal O}(10^{-3})$.
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