• cosmological perturbation theory
• geodesic light-cone gauge

In this thesis we develop a cosmological perturbation theory adapted to the light-cone structure. We start by building general perturbations on the top of a background described by a Geodesic Light-Cone (GLC) set of coordinates. We provide decomposition in terms of Scalars and PseudoScalars (SPS) which may also be applied to non-standard backgrounds. We first study the gauge transformation properties of the SPS perturbations. Thereafter, enjoying of exact expressions for cosmological observables within the GLC gauge fixing obtained through a covariant approach, we provide a general recipe to the evaluation of linearized gauge invariant observables. Then, we apply this recipe to the angular distance-redshift relation, rendering a simple and gauge invariant expression. Furthermore, we develop a formalism to classify general perturbations directly according to their helicity instead of the background symmetries which classifies the perturbations into Scalar-Vector-Tensor (SVT) degrees of freedom. Thereafter, we use this formalism to show how our SPS decomposition directly decomposes the light-cone structure into $E$ and $B$ modes of the perturbations, and we show how our SPS decomposition relates to the SVT one. Finally, we provide simplified evolution equations within the gradient expansion approximation, which is an important step in the evaluation of backreaction on the expansion rate using light-cone averages during primordial epochs.