CMB Anisotropies at Second-Order II: Analytical Approach

We provide an analytical approach to the second–order Cosmi c Microwave Background (CMB) anisotropies generated by the non–linear dynamics taking p lace at last scattering. We study the acoustic oscillations of the photon–baryon fluid in the tigh t coupling limit and we extend at second– order the Meszaros effect. We allow for a generic set of initia l conditions due to primordial non- Gaussianity and we compute all the additional contribution s arising at recombination. Our results are useful to provide the full second–order radiation trans fer function at all scales necessary for establishing the level of non-Gaussianity in the CMB