Spectral distortions in the cosmic microwave background polarization
  We compute the spectral distortions of the Cosmic Microwave Background (CMB)
polarization induced by non-linear effects in the Compton interactions between
CMB photons and cold intergalactic electrons. This signal is of the $y$-type
and is dominated by contributions arising from the reionized era. We stress
that it is not shadowed by the thermal SZ effect which has no equivalent for
polarization. We decompose its angular dependence into $E$- and $B$-modes, and
we calculate the corresponding power spectra, both exactly and using a suitable
Limber approximation that allows a simpler numerical evaluation. We find that
$B$-modes are of the same order of magnitude as $E$-modes. Both spectra are
relatively flat, peaking around $\ell=280$, and their overall amplitude is
directly related to the optical depth to reionization. Moreover, we find this
effect to be one order of magnitude larger than the non-linear kinetic
Sunyaev-Zel'dovich effect in galaxy clusters. Finally, we discuss how to
improve the detectability of our signal by cross-correlating it with other
quantities sourced by the flow of intergalactic electrons.
