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.
