Secondary CMB anisotropies from the kinetic SZ effect

The reionization of the universe by stars and quasars is expected to be a highly inhomogeneous process. Moreover, the fluctuations of the matter density field also lead to inhomogeneities of the free electron distribution. These patterns gave rise to secondary CMB anisotropies through Thomson scattering of photons by free electrons. In this article we present an analytic model, based on our previous work which tackled the reionization history of the universe, which allows us to describe the generation of these secondary CMB anisotropies. We take into account the "patchy pattern" of reionization (HII bubbles), the cross-correlations of these ionized regions, the small-scale fluctuations of the matter density field and the contribution from collapsed objects. For an open universe, we find that the angular correlation function C(theta) displays a very slow decline from C(0) similar to 6 10(-13) up to the scale theta similar to 10(-3) rad where it shows a sharp drop. On the other hand, the power-spectrum l(l + 1)C-l/(2 pi) (and the "local average" S-l) exhibits a plateau of height similar to 10(-13) in the range 10(3) < l < 10(6). We find that for large wavenumbers l > 10(4) the signal is dominated by the contribution from collapsed halos while for l > 10(4) it is governed by the large-scale correlations of HII bubbles. This implies that one cannot discriminate reionization by stars from a quasar-driven scenario since the size of ionized regions never dominates the behaviour of the anisotropies. Moreover, the secondary CMB anisotropies arise from a broad range of redshifts (7.5 < z < 10 for the IGM and 0 < z < 7 for galactic halos). Thus, we find that the generation of these anisotropies involves several intricate processes and they are close to the resolution limit of current numerical simulations. The signal expected in our model might bias the cosmological parameter estimation from CMB experiments such as Planck or MAP, and could be detected by future mm-wavelength interferometers (e.g., ALMA).