CMB anisotropies from patchy reionisation and diffuse Sunyaev-Zel'dovich
  effects
  Anisotropies in the Cosmic Microwave Background (CMB) can be induced during
the later stages of cosmic evolution, and in particular during and after the
Epoch of Reionisation. Inhomogeneities in the ionised fraction, but also in the
baryon density, in the velocity fields and in the gravitational potentials are
expected to generate correlated CMB perturbations. We present a complete
relativistic treatment of all these effects, up to second order in perturbation
theory, that we solve using the numerical Boltzmann code SONG. The physical
origin and relevance of all second order terms are carefully discussed. In
addition to collisional and gravitational contributions, we identify the
diffuse analogue of the blurring and kinetic Sunyaev-Zel'dovich (SZ) effects.
Our approach naturally includes the correlations between the imprint from
patchy reionisation and the diffuse SZ effects thereby allowing us to derive
reliable estimates of the induced temperature and polarisation CMB angular
power spectra. In particular, we show that the B-modes generated at
intermediate length-scales (l~100) have the same amplitude as the B-modes
coming from primordial gravitational waves with a tensor-to-scalar ratio
r=10^{-4}.
