Gauge invariance on the light-cone: curvature perturbations and radiative degrees of freedom

We derive the expressions on the observed light-cone for some relevant cosmological gauge invariant variables, such as the Mukhanov-Sasaki variable and E- and B- modes of the tensor perturbations. Since the structure of the light-cone does not reflect in a direct way the FLRW symmetries, we develop a formalism which is coordinate independent and classifies the perturbations according to their helicities. Even though we work with linear perturbations, our formalism can be readily extended to non-linear theory and put the basis to study the evolution of cosmological perturbations, since the early-until the late-time Universe, directly along the observed light-cone.