The maximum B-mode polarization of the cosmic microwave background from inhomogeneous reionization

We compute the B-mode polarization power spectrum of the cosmic microwave background from an epoch of inhomogeneous reionization, using a simple model in which H II regions are represented by ionized spherical bubbles with a lognormal distribution of sizes whose clustering properties are determined by large-scale structure. Both the global ionization fraction and the characteristic radius of H II regions are allowed to be free functions of redshift. Models that would produce substantial contamination in degree-scale gravitational wave B-mode measurements have power that is dominated by the shot noise of the bubbles. Rare bubbles of radius greater than or similar to 100 Mpc at z > 20 can produce signals that in fact exceed the B-modes from gravitational lensing and are comparable to the maximal allowed signal of gravitational waves (similar to 0.1 mu K) while still being consistent with global constraints on the total optical depth. Even bubbles down to 20 Mpc at z similar to 15, or 40 Mpc at z similar to 10, can be relevant (0.01 mu K) once the lensing signal is removed, either statistically or directly. However, currently favored theoretical models that have ionization bubbles that only grow to such sizes at the very end of a fairly prompt and late reionization produce signals that are at most at these levels.