Inferences of $H_0$ in presence of a non-standard recombination
  Measurements of the Hubble parameter from the distance ladder are in tension
with indirect measurements based on the cosmic microwave background (CMB) data
and the inverse distance ladder measurements at 3-4 $\sigma$ level. We consider
phenomenological modification to the timing and width of the recombination
process and show that they can significantly affect this tension. This
possibility is appealing, because such modification affects both the distance
to the last scattering surface and the calibration of the baryon acoustic
oscillations (BAO) ruler. Moreover, because only a very small fraction of the
most energetic photons keep the early universe in the plasma state, it is
possible that such modification could occur without affecting the energy
density budget of the universe or being incompatible with the very tight limits
on the departure from the black-body spectrum of CMB. In particular, we find
that under this simplified model, with a conservative subset of Planck data
alone, $H_0=73.44_{-6.77}^{+5.50}~{\rm km\ s}^{-1}\ {\rm Mpc}^{-1}$ and in
combination with BAO data $H_0=68.86_{-1.35}^{+1.31}~{\rm km\ s}^{-1}\ {\rm
Mpc}^{-1}$, decreasing the tension to $\sim 2\sigma$ level. However, when
combined with Planck lensing reconstruction and high-$\ell$ polarization data,
the tension climbs back to $\sim 2.7\sigma$, despite the uncertainty on
non-ladder $H_0$ measurement more than doubling.
