Nicola Bartolo

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 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.

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.

We present the computation of the full system of Boltzmann equations at second order describing the evolution of the photon, baryon and cold dark matter fluids. These equations allow one to follow the time evolution of the cosmic microwave background anisotropies at second order at all angular scales from the early epoch, when the cosmological perturbations were generated, to the present, through the recombination era. This paper sets the stage for the computation of the full second-order radiation transfer function at all scales and for a generic set of initial conditions specifying the level of primordial non-Gaussianity. In a companion paper, we will present the computation of the three-point correlation function at recombination which is very relevant for the issue of non-Gaussianity in the cosmic microwave background anisotropies.

We present the computation of the full system of Boltzmann equations at second-order describing the evolution of the photon, baryon and cold dark matter fluids. These equations allow to follow the time evolution of the Cosmic Microwave Background (CMB) anisotropies at second-order at all angular scales from the early epoch, when the cosmological perturbations were generated, to the present through the recombination era. This paper sets the stage for the computation of the full second-order radiation transfer function at all scales and for a a generic set of initial conditions specifying the level of primordial non-Gaussianity. In a companion paper, we will present the computation of the three-point correlation function at recombination which is so relevant for the issue of non-Gaussianity in the CMB anisotropies.

We calculate the full second-order radiation transfer function for Cosmic Microwave Background anisotropies on large angular scales in a flat universe filled with matter and cosmological constant. It includes (i) the second-order generalization of the Sachs-Wolfe effect, and of (ii) both the early and late Integrated Sachs-Wolfe effects, (iii) the contribution of the second-order tensor modes, and is valid for a generic set of initial conditions specifying the level of primordial non-Gaussianity.

We investigate the possibility that the amplitude of scalar density perturbations may be damped after inflation. This would imply that CMB anisotropies do not uniquely fix the amplitude of the perturbations generated during inflation and that the present tensor-to-scalar ratio might be larger than produced in inflation, increasing the prospects of detection of primordial gravitational radiation. It turns out, however, that the damping of density perturbations is hard to achieve.

We compute the fully non-linear Cosmic Microwave Background (CMB) anisotropies on scales larger than the horizon at last-scattering in terms of only the curvature perturbation, providing a generalization of the linear Sachs-Wolfe effect at any order in perturbation theory. We show how to compute the n-point connected correlation functions of the large-scale CMB anisotropies for generic primordial seeds provided by standard slow-roll inflation as well as the curvaton and other scenarios for the generation of cosmological perturbations. As an application of our formalism, we compute the three- and four-point connected correlation functions whose detection in future CMB experiments might be used to assess the level of primordial non-Gaussianity, giving the theoretical predictions for the parameters of quadratic and cubic non-linearities f_NL and g_NL.