Cosmological Observations: Averaging on the Null Cone
  The universe is not isotropic or spatially homogeneous on local scales. The
averaging of local inhomogeneities in general relativity can lead to
significant dynamical effects on the evolution of the universe and on the
interpretation of cosmological data. In particular, all deductions about
cosmology are based on light paths; averaging can have an important effect on
photon propagation and hence cosmological observations. It would be desirable
to describe the physical effects of averaging in terms of observational
quantities and focussing on the behaviour of light. Data (e.g., matter terms,
such as the density or galaxy number counts, which are already expressed as
averaged quantities) is given on the null cone. Therefore, it is
observationally meaningful to consider light-cone averages of quantities. In
principle, we wish to describe the cosmological equations on the null cone, and
hence we need to construct the averaged geometry on the null cone. However, we
argue that it is still necessary to average the full Einstein field equations
to obtain suitably averaged equations on the null cone. Since it is not the
geometry per se that appears in the observational relations, we discuss whether
it is possible to covariantly `average' just a subset of the evolution
equations on the null cone, focussing on relevant observational quantities. We
present an averaged version of the scalar null Raychaudhuri equation, which may
be a useful first step in this regard.
