  Cosmological models typically neglect the complicated nature of the spacetime
manifold at small scales in order to hypothesize idealized general relativistic
solutions for describing the average dynamics of the Universe. Although these
solutions are remarkably successful in accounting for data, they introduce a
number of puzzles in cosmology, and their foundational assumptions are
therefore important to test. In this paper, we go beyond the usual assumptions
in cosmology and propose a formalism for averaging the local general
relativistic spacetime on an observer's past null cone: we formulate average
properties of light fronts as they propagate from a cosmological emitter to an
observer. The energy-momentum tensor is composed of an irrotational dust source
and a cosmological constant -- the same components as in the $\Lambda$CDM model
for late cosmic times -- but the metric solution is not \emph{a
priori}constrained to be locally homogeneous or isotropic. This generally makes
the large-scale dynamics depart from that of a simple Friedmann--Lema\^\i
tre--Robertson--Walker solution through \emph{backreaction} effects. Our
formalism quantifies such departures through a fully covariant system of
area-averaged equations on the light fronts propagating towards an observer,
which can be directly applied to analytical and numerical investigations of
cosmic observables. For this purpose, we formulate light front averages of
observable quantities, including the effective angular diameter distance and
the cosmological redshift drift and we also discuss the backreaction effects
for these observables.
