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We compute the B-mode polarization power spectrum of the CMB from an epoch ofinhomogeneous reionization, using a simple model in which HII regions arerepresented by ionized spherical bubbles with a log normal distribution ofsizes whose clustering properties are determined by large-scale structure. Boththe global ionization fraction and the characteristic radius of HII regions areallowed to be free functions of redshift. Models that would produce substantialcontamination to degree scale gravitational wave B-mode measurements have powerthat is dominated by the shot noise of the bubbles. Rare bubbles of >100 Mpc atz>20 can produce signals that in fact exceed the B-modes from gravitationallensing and are comparable to the maximal allowed signal of gravitational waves(~0.1uK) while still being consistent with global constraints on the totaloptical depth. Even bubbles down to 20 Mpc at z~15, or 40 Mpc at z~10 can berelevant (0.01uK) once the lensing signal is removed either statistically ordirectly. However, currently favored theoretical models that have ionizationbubbles that only grow to such sizes at the very end of a fairly prompt andlate reionization produce signals which are at most at these levels.Comment: 14 pages, 11 figures; published in ApJ; corrected Fig. 4 and updated  reference

The MaximumB‐Mode Polarization of the Cosmic Microwave Background from Inhomogeneous Reionization