Patchy Screening of the Cosmic Microwave Background by Inhomogeneous Reionization

We derive a constraint on patchy screening of the cosmic microwave background from inhomogeneous reionization, using off-diagonal TB and TT correlations in WMAP-7 temperature/polarization data. We interpret this as a constraint on the rms optical-depth fluctuation \Delta\tau\ as a function of a coherence multipole Lc. We relate these parameters to a comoving coherence scale, of bubble size Rc, in a phenomenological model where reionization is instantaneous but occurs on a crinkly surface, and also to the bubble size in a model of "Swiss cheese" reionization where bubbles of fixed size are spread over some range of redshifts. The current WMAP data are still too weak, by several orders of magnitude, to constrain reasonable models, but forthcoming Planck and future EPIC data should begin to approach interesting regimes of parameter space. We also present constraints on the parameter space imposed by the recent results from the EDGES experiment.