Secondary CMB anisotropies from the kinetic SZ effect
  We present an analytic model, based on previous works which tackled the reionization history of the universe, which allows us to describe the generation of the secondary CMB anisotropies due to the kinetic SZ effect. 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 power-spectrum $l(l+1)C_l/(2\pi)$ exhibits a plateau of height $10^{-13}$ 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). The signal expected in our model might bias the cosmological parameter estimation from CMB experiments such as Planck and could be detected by future mm-wavelength interferometers (e.g., ALMA). 
P. Valageas, A. Balbi, J. Silk