Evolution of Second-Order Cosmological Perturbations and Non-Gaussianity

We present a second-order gauge-invariant formalism to study the evolution of curvature perturbations in a Friedmann–Robertson–Walker universe filled by multiple interacting fluids. We apply such a general formalism to describe the evolution of the second-order curvature perturbations in the standard one-single-field inflation, in the curvaton and in the inhomogeneous reheating scenarios for the generation of the cosmological perturbations. Moreover, we provide the exact expression for the second-order temperature anisotropies on large scales, including second-order gravitational effects and extend the well known formula for the Sachs–Wolfe effect at linear order. Our findings clarify what is the exact non-linearity parameter fNL entering in the determination of higher-order statistics such as the bispectrum of Cosmic Microwave Background temperature anisotropies. Finally, we compute the level of non-Gaussianity in each scenario for the creation of cosmological perturbations.