• cosmological perturbation theory
• deltaN formalism
• geodesic light-cone coordinates
• inflation
• observational synchronous gauge

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.