Constraints on perturbations to the recombination history from
  measurements of the CMB damping tail
  The primordial CMB at small angular scales is sensitive to the ionization and
expansion history of the universe around the time of recombination. This
dependence has been exploited to constrain the helium abundance and the
effective number of relativistic species. Here we focus on allowed ionization
fraction trajectories, $\Xe (z)$, by constraining low-order principal
components of perturbations to the standard recombination scenario
($\Xe$-eigenmodes) in the circa 2011 SPT, ACT and WMAP7 data. Although the
trajectories are statistically consistent with the standard recombination, we
find that there is a tension similar to that found by varying the helium
fraction. As this paper was in press, final SPT and ACT datasets were released
and we applied our framework to them: we find the tension continues, with
slightly higher significance, in the new 2012 SPT data, but find no tension
with the standard model of recombination in the new 2012 ACT data. We find that
the prior probabilities on the eigenamplitudes are substantially influenced by
the requirement that $\Xe$ trajectories conserve electron number. We propose
requiring a sufficient entropy decrease between posterior and prior
marginalized distributions be used as an $\Xe$-mode selection criterion. We
find that in the case of the 2011 SPT/ACT+WMAP7 data only two modes are
constrainable, but upcoming ACTPol, Planck and SPTPol data will be able to test
more modes and more precisely address the current tension.
