deltaN Formalism and Second Order Perturbation Theory on the Light-Cone

In this master’s thesis, we build a second order cosmological perturbation theory on top of a background geometry expressed using the so-called Geodesic Light-Cone (GLC) coordinates, going beyond the first order analysis already present in literature. In particular, we study for the first time the gauge transformations of second order perturbative functions on the light-cone and, after a proper matching with standard perturbation theory, we find the second order standard gauge fixing which corresponds to the GLC gauge, called Observational Synchronous Gauge. Afterwards, working within the inflationary scenario, we apply this perturbative scheme to compute, at second order in the GLC perturbations, the conserved curvature perturbation ζ, which encodes the dynamics of quantum scalar fluctuations generated in the primordial Universe. To conclude, by exploiting recent developments regarding the separate universe approach and the δN formalism on the light-cone, we verify that the standard, uppermost formula δN = −ζ still holds on the light-cone at second order in perturbation theory.