On the contamination of the global 21~cm signal from polarized
  foregrounds
  Global (i.e. sky-averaged) $21$~cm signal experiments can measure the
evolution of the universe from the Cosmic Dawn to the Epoch of Reionization.
These measurements are challenged by the presence of bright foreground emission
that can be separated from the cosmological signal if its spectrum is smooth.
This assumption fails in the case of single polarization antennas as they
measure linearly polarized foreground emission - which is inevitably Faraday
rotated through the interstellar medium. We investigate the impact of Galactic
polarized foregrounds on the extraction of the global 21~cm signal through
realistic sky and dipole simulations both in a low frequency band from $50$ to
$100$~MHz, where a 21~cm absorption profile is expected, and in a higher
frequency band ($100-200$~MHz). We find that the presence of a polarized
contaminant with complex frequency structure can bias the amplitude and the
shape of the reconstructed signal parameters in both bands. We investigate if
polarized foregrounds can explain the unexpected $21$~cm Cosmic Dawn signal
recently reported by the EDGES collaboration. We find that unaccounted
polarized foreground contamination can produce an enhanced and distorted
$21$~cm absorption trough similar to the anomalous profile reported by Bowman
et al. (2018), and whose amplitude is in mild tension with the assumed input
Gaussian profile (at $\sim 1.5 \sigma$ level). Moreover, we note that, under
the hypothesis of contamination from polarized foreground, the amplitude of the
reconstructed EDGES signal can be overestimated by around $30\%$, mitigating
the requirement for an explanation based on exotic physics.
