|We review some theoretical and statistical aspects of the origin of the large-scale structure in the Universe, in view of the two most widely known and accepted scenarios: the inflaton and the curvaton scenarios. Among the theoretical aspects, we point out the impossibility of having a low inflationary energy scale in the simplest curvaton model. A couple of modifications to the simplest setup are explored, corresponding to the implementation of a second (thermal) inflationary period whose end makes the curvaton field `heavy', triggering either its oscillations or immediate decay.
Low scale inflation is then possible to attain with H_\ast being as low as 1 TeV. Among the statistical aspects, we study the bispectrum B_\zeta(k_1,k_2,k_3) of the primordial curvature perturbation \zeta whose normalisation \fnl gives information about the level of non-gaussianity in \zeta. In connection with \fnl, several conserved and/or gauge invariant quantities described as the second-order curvature perturbation have been given in the literature. We review each of these quantities showing how to interpret one in terms of the others, and analyze the respective expected \fnl in both the inflaton and the curvaton scenarios as well as in other less known models for the generation of primordial perturbations and/or non-gaussianities.
The \delta N formalism turns out to be a powerful technique to compute \fnl in multi-component slow-roll inflation, as the knowledge of the evolution of some family of unperturbed universes is the only requirement. We present for the first time this formalism and apply it to selected examples.