Variations in fundamental constants at the cosmic dawn
  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 ${\cal O}(10^{-3})$.
