CMB anisotropies at second-order II: analytical approach

We provide an analytical approach to the second-order cosmic microwave background (CMB) anisotropies generated by the non-linear dynamics taking place at last scattering. We study the acoustic oscillations of the photon-baryon fluid in the tight coupling limit and we extend at second order the Meszaros effect. We allow for a generic set of initial conditions due to primordial non-Gaussianity and we compute all of the additional contributions arising at recombination. Our results are useful to provide the full second-order radiation transfer function at all scales necessary for establishing the level of non-Gaussianity in the CMB.