Light-cone averaging in cosmology: formalism and applications

We present a general gauge invariant formalism for defining cosmological averages that are relevant for observations based on light-like signals. Such averages involve either null hypersurfaces corresponding to a family of past light-cones or compact surfaces given by their intersection with timelike hypersurfaces. Generalized Buchert-Ehlers commutation rules for derivatives of these light-cone averages are given. After introducing some adapted ``geodesic light-cone'' coordinates, we give explicit expressions for averaging the redshift to luminosity-distance relation and the so-called ``redshift drift'' in a generic inhomogeneous Universe.