• 2+1+1 formalism
• averaging formalism
• cosmological backreaction
• geodesic light-cone coordinates

In mainstream cosmology, small-scale inhomogeneities are usually treated as perturbations to a homogeneous and isotropic background, implicitly assuming an averaging operation that "smoothes them out". However, the nonlinearity of Einstein's equations implies that averaging and dynamic evolution do not commute, leading to a "backreaction mechanism" where inhomogeneities affect the large-scale dynamics of the averaged geometry. In this master's thesis, we account for the complicated nature of spacetime at small scales by studying integral properties, specifically by employing a covariant and gauge-invariant averaging operation on the observer's past light-cone. This reflects the fact that cosmological observations rely mostly on light-like signals. Specifically, by foliating the null cone into a family of spatial two-spheres, referred to as screen spaces and identified by specific values of the redshift, we formulate dynamical equations describing the effective evolution of the Universe. Going in order, we first provide a general prescription for foliating the observer's past light-cone, offering an alternative notion of the screen spaces in terms of a projection tensor and deriving evolution and constraint equations governing the dynamics of the 2-spheres. We then define an effective scale factor, intimately related to the surface area of the screen space, and we formulate effective dynamical equations describing its evolution. Finally, we numerically evaluate the expansion law for this effective scale factor under a stochastic spectrum of inhomogeneities, considering the contributions obtained going up to the second order in perturbation theory. In particular, we consider a spatially flat FLRW universe, focusing on a CDM scenario.