Secondary cosmic microwave background anisotropies in a universe reionizedin patches

In a universe reionized in patches! the Doppler effect from Thomson scatter ing off free electrons generates secondary cosmic microwave background (CMB ) anisotropies. For a simple model with small patches and late reionization , we analytically calculate the anisotropy power spectrum. Patchy reionizat ion can, in principle, be the main source of anisotropies on arcminute scal es. On larger angular scales, its contribution to the CMB power spectrum is a small fraction of the primary signal and is only barely detectable in th e power spectrum with even an ideal, i.e., cosmic variance limited, experim ent and an extreme model of reionization. Consequently, patchy reionization is unlikely to affect cosmological parameter estimation from the acoustic peaks in the CMB. Its detection on small angles would help determine the io nization history of the universe, in particular, the typical size of the io nized region and the duration of the reionization process.