Cosmic Microwave Background Constraints in Light of Priors Over
  Reionization Histories
  Non-parametric reconstruction or marginalization over the history of
reionization using cosmic microwave background data necessarily assumes a prior
over possible histories. We show that different but reasonable choices of
priors can shift current and future constraints on the reionization optical
depth, $\tau$, or correlated parameters such as the neutrino mass sum, $\Sigma
m_\nu$, at the level of 0.3-0.4$\sigma$, i.e., that this analysis is somewhat
prior dependent. We point out some prior-related problems with the commonly
used principal component reconstruction, concluding that the significance of
some recent hints of early reionization in Planck 2015 data has been
overestimated. We also present the first non-parametric reconstruction applied
to newer Planck intermediate (2016) data and find that the hints of early
reionization disappear entirely in this more precise dataset. These results
limit possible explanations of the EDGES 21cm signal which would have also
significantly reionized the universe at $z\,{>}\,15$. Our findings about the
dependence on priors motivate the pursuit of improved data or searches for
physical reionization models which can reduce the prior volume. The discussion
here of priors is of general applicability to other non-parametric
reconstructions, for example of the primordial power spectrum, of the
recombination history, or of the expansion rate.
